Problem
stringlengths 11
628
| Rationale
stringlengths 1
2.74k
| options
stringlengths 37
137
| correct
stringclasses 5
values | annotated_formula
stringlengths 6
848
| linear_formula
stringlengths 7
357
| category
stringclasses 6
values |
|---|---|---|---|---|---|---|
a batsman makes a score of 50 runs in the 6 th inning and thus increases his average by 2 . find his average after 6 th inning . | "72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d" | a ) 354517481 , b ) 457687783 , c ) 246567689 , d ) 725117481 , e ) 565776879 | d | multiply(subtract(9999, const_4), 72519) | subtract(n1,const_4)|multiply(#0,n0)| | general |
tim and Γ© lan are 60 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and Γ© lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets Γ© lan ? | "ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 49 / 64 - - > ( x - 12 ) ^ 2 = 49 / 64 x ^ 2 square rooting u have x - 12 / x = 7 / 8 or x = 96 d" | a ) 24 , b ) 48 , c ) 60 , d ) 96 , e ) 84 | d | divide(12, subtract(const_1, sqrt(divide(49, 64)))) | divide(n2,n3)|sqrt(#0)|subtract(const_1,#1)|divide(n0,#2)| | other |
tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 9 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ? | option ' c ' | a ) 41 , b ) 39 , c ) 43 , d ) 45 , e ) 47 | c | subtract(multiply(15, 43), add(multiply(7, 41), multiply(7, 45))) | multiply(n0,n1)|multiply(n2,n3)|multiply(n2,n5)|add(#1,#2)|subtract(#0,#3) | general |
a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 9 are wrong and the other digits are correct , then the correct answer would be : | p = 432 ( 100 / 5 ) ^ 2 = > p = 10800 answer : e | a ) 2277 , b ) 2667 , c ) 3600 , d ) 9766 , e ) 10800 | e | divide(432, subtract(power(add(divide(20, const_100), const_1), 2), add(multiply(divide(20, const_100), 2), const_1))) | divide(n1,const_100)|add(#0,const_1)|multiply(n0,#0)|add(#2,const_1)|power(#1,n0)|subtract(#4,#3)|divide(n2,#5) | gain |
how many seconds does sandy take to cover a distance of 600 meters , if sandy runs at a speed of 15 km / hr ? | explanation : there is more than 1 way to approach the solution ; however , i will detail the easiest way to go about it here . we want to find the ratio of time taken for nth round : time taken for ( n - 1 ) th round it will be same as finding the ratio of time taken for 2 nd round : time taken for 1 st round . 1 round = circumference of the circle = 2 Ο r 1 st round : speed = Ο r for 30 seconds . so , total distance travelled = Ο r / 2 . speed = Ο r / 2 for 1 minute . so , total distance travelled = Ο r / 2 . speed = Ο r / 4 for 2 minutes . so , total distance travelled = Ο r / 2 . speed = Ο r / 8 for 4 minutes . so , total distance travelled = Ο r / 2 . so , for a distance of 2 Ο r , time taken is 7.5 minutes . 2 nd round : speed = Ο r / 16 for 8 minutes . so , total distance travelled = Ο r / 2 . speed = Ο r / 32 for 16 minutes . so , total distance travelled = Ο r / 2 . speed = Ο r / 64 for 32 minutes . so , total distance travelled = Ο r / 2 . speed = Ο r / 128 for 64 minutes . so , total distance travelled = Ο r / 2 . so , for a distance of 2 Ο r , time taken is 120 minutes . ratio is 120 : 7.5 = 16 : 1 . answer : c | a ) 4 , b ) 8 , c ) 16 , d ) 32 , e ) 36 | c | power(2, 4) | power(n1,n2) | physics |
what is x if x + 5 y = 24 and y = 2 ? | "1028 / 4 = 257 kmph answer : d" | a ) 104 , b ) 255 , c ) 266 , d ) 257 , e ) 276 | d | divide(1028, 4) | divide(n0,n1)| | physics |
convert 100 miles into inches ? | "2550 - - - - 400 100 - - - - ? = > 15 % answer : c" | a ) 18 , b ) 10 , c ) 15 , d ) 66 , e ) 41 | c | multiply(divide(subtract(2550, 2130), 2550), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)| | gain |
a certain no . when divided by 80 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ? | "4 * ( - 3 ) = 4 * ( - 3 ) - 2 ( 4 + ( - 3 ) ) = - 12 - 2 = - 14 option ( a )" | a ) β 14 , b ) β 11 , c ) β 4 , d ) 4 , e ) 16 | a | add(negate(multiply(add(negate(3), 4), 2)), multiply(negate(3), 4)) | negate(n2)|add(n1,#0)|multiply(n1,#0)|multiply(#1,n0)|negate(#3)|add(#2,#4)| | general |
the pressure someone experiences as he or she dives deeper and deeper in the ocean increases linearly . on the surface , the pressure is close to 15 pounds per square inch . 33 feet below the surface , the pressure is 30 pounds . if 25000 pounds per sq inch can crush your bones , what depth is extremely dangerous for humans ? | "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )" | a ) t = 16 , b ) t = 32 , c ) t = 64 , d ) 128 , e ) 512 | b | multiply(8, 4) | multiply(n0,n3)| | geometry |
if 0.2 of a number is equal to 0.08 of another number , the ratio of the numbers is : | 2 nd day he earns = 3 ( 2 β 5 ) 3 rd day he earns = 3 ( 3 β 5 ) on 20 th day he earns 3 ( 20 - 5 ) = 45 rupees answer : d | a ) 21 , b ) 22 , c ) 20 , d ) 45 , e ) 30 | d | subtract(multiply(5, 10), 5) | multiply(n0,n1)|subtract(#0,n0) | physics |
the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 1323 sq m , then what is the breadth of the rectangular plot ? | "solution : let xx be the number he chose , then 3 β
x β 138 = 102 3 x = 240 x = 80 answer a" | a ) 80 , b ) 120 , c ) 130 , d ) 140 , e ) 150 | a | divide(add(102, 138), 3) | add(n1,n2)|divide(#0,n0)| | general |
if | x - 20 | = 40 what is the sum of all the values of x . | solution relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec total distance covered = ( 500 + 500 ) m = 1000 m required time = ( 1000 x 6 / 125 ) sec = 48 sec answer c | a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) none | c | multiply(divide(500, divide(multiply(const_1000, add(45, 30)), const_3600)), const_2) | add(n1,n2)|multiply(#0,const_1000)|divide(#1,const_3600)|divide(n0,#2)|multiply(#3,const_2) | physics |
a batsman makes a score of 50 runs in the 6 th inning and thus increases his average by 2 . find his average after 6 th inning . | formula : ( after = 100 denominator ago = 100 numerator ) 14300 Γ 115 / 100 Γ 115 / 100 = 18911 a | a ) 18911 , b ) 18788 , c ) 19898 , d ) 14000 , e ) 14400 | a | multiply(14300, power(add(const_1, divide(15, const_100)), 2)) | divide(n1,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2) | gain |
tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 10 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ? | "first of all | x - 3 | ^ 2 = ( x - 3 ) ^ 2 , so we have : ( x - 3 ) ^ 2 + | x - 3 | = 20 . when x < 3 , x - 3 is negative , thus | x - 3 | = - ( x - 3 ) . in this case we ' ll have ( x - 3 ) ^ 2 - ( x - 3 ) = 20 - - > x = - 1 or x = 8 . discard x = 8 because it ' s not in the range we consider ( < 3 ) . when x > = 3 , x - 3 is non - negative , thus | x - 3 | = x - 3 . in this case we ' ll have ( x - 3 ) ^ 2 + ( x - 3 ) = 20 - - > x = - 2 or x = 7 . discard x = - 2 because it ' s not in the range we consider ( > = 3 ) . thus there are two solutions : x = - 1 and x = 7 - - > the sum = 6 . answer : b ." | a ) - 1 , b ) 6 , c ) 7 , d ) 12 , e ) 14 | b | add(add(const_4, 3), subtract(3, const_4)) | add(n0,const_4)|subtract(n0,const_4)|add(#0,#1)| | general |
the average age of a class of 24 students is 23 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ? | i got the same thing b is the answer 8 or 20 | a ) 8 and 9 , b ) 8 and 20 , c ) 17 and 21 , d ) 12 and 29 , e ) 17 and 29 | b | add(multiply(subtract(add(subtract(9, 5), sqrt(subtract(power(subtract(9, 5), 5), multiply(5, multiply(9, 5))))), 3), const_10), subtract(subtract(subtract(9, 5), sqrt(subtract(power(subtract(9, 5), 5), multiply(5, multiply(9, 5))))), 3)) | multiply(n0,n1)|subtract(n1,n0)|multiply(n0,#0)|power(#1,n3)|subtract(#3,#2)|sqrt(#4)|add(#5,#1)|subtract(#1,#5)|subtract(#6,n4)|subtract(#7,n4)|multiply(#8,const_10)|add(#10,#9)| | general |
the measurement of a rectangular box with lid is 25 cmx 6 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of Ο cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere ) | "speed = x and y resp length of first = 27 x length of second train = 17 y related speed = x + y time taken to cross each other = 23 s 27 x + 17 y / x + y = 23 27 x + 17 y = 23 ( x + y ) 4 x = 6 y x / y = 6 / 4 = 3 / 2 answer b" | a ) 1 : 2 , b ) 3 : 2 , c ) 3 : 1 , d ) 1 : 3 , e ) 1 : 4 | b | divide(subtract(27, 23), subtract(23, 17)) | subtract(n0,n2)|subtract(n2,n1)|divide(#0,#1)| | physics |
a , b and c started a business with a total investment of rs . 72000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find a ' s share . | 36 pie cubic feet of water and its filled to half tank ' s capacity . . . volume of tank = 72 pie cubic feet height of tank = 4 * 2 = 8 feet ( since tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . ) 72 pie = pie * r 2 * 8 r 2 = 9 r = 3 feet answer : d | ['a ) 0 feet', 'b ) 1 feet', 'c ) 2 feet', 'd ) 3 feet', 'e ) 4 feet'] | d | sqrt(divide(divide(multiply(36, const_pi), 4), const_pi)) | multiply(n0,const_pi)|divide(#0,n1)|divide(#1,const_pi)|sqrt(#2) | geometry |
a man can row at 5 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ? | 3 / 4 = 3 x / 4 x we need to find out ( 3 x + 5 ) / ( 4 x + 5 ) off course we can not solve this to arrive at any rational number hence e . | a ) 3 / 4 , b ) 8 / 9 , c ) 18 / 19 , d ) 23 / 24 , e ) it can not be determined from the information given | e | divide(3, 4) | divide(n0,n1) | other |
a certain roller coaster has 3 cars , and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 3 times , what is the probability that the passenger will ride in each of the 3 cars ? | "let d initial price be 100 33 % rise now price = 133 / 100 * 100 = 133 10 % discount then price = 133 * 90 / 100 = 119.7 15 % discount then price = 119.7 * 85 / 100 = 101.745 so gain = 101.745 - 100 = 1.745 gain % = gain * 100 / cp = = > 1.745 * 100 / 100 = 1.745 % answer : a" | a ) 1.745 % , b ) 4.745 % , c ) 3.745 % , d ) 6.745 % , e ) 7.745 % | a | subtract(multiply(multiply(add(const_100, 33), divide(subtract(const_100, 10), const_100)), divide(subtract(const_100, 15), const_100)), const_100) | add(n0,const_100)|subtract(const_100,n2)|subtract(const_100,n1)|divide(#1,const_100)|divide(#2,const_100)|multiply(#0,#4)|multiply(#3,#5)|subtract(#6,const_100)| | gain |
how many of the positive factors of 24 are not factors of 27 | "let us assume the number of dogs , cats and bunnies to be 3 x , 7 x and 13 x total dogs and bunnies = 16 x . and we are given that 16 x = 352 . hence x = 22 . dogs = 3 x = 3 * 22 = 66 ( option b )" | a ) 42 , b ) 66 , c ) 98 , d ) 112 , e ) 154 | b | multiply(divide(352, add(3, 13)), 3) | add(n0,n2)|divide(n3,#0)|multiply(n0,#1)| | other |
if 5 < x < 9 and y = x + 3 , what is the greatest possible integer value of x + y ? | "answer let the number be x . x / 15 = 240 / x x ^ 2 = 240 * 15 = 3600 x = β 3600 = 60 correct option : c" | a ) 48 , b ) 75 , c ) 60 , d ) 54 , e ) 45 | c | divide(add(240, 15), const_2) | add(n0,n1)|divide(#0,const_2)| | general |
how many bricks , each measuring 25 cm * 11.25 cm * 6 cm , will be needed to build a wall 8 m * 6 m * 22.5 m | "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 25 % , the new price is 0.75 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.75 p ) ( 1.8 n ) = 1.35 np , which is 1.35 times the old revenue , so is 35 % greater . answer : a" | a ) 35 % increase , b ) 44 % decrease , c ) 60 % increase , d ) 66 % increase , e ) 66 % decrease | a | subtract(divide(multiply(add(80, const_100), subtract(const_100, 25)), const_100), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(#3,const_100)| | gain |
in a class of 42 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ? | explanation : ( a + b ) , five years ago = ( 15 * 2 ) = 30 years . ( a + b ) , now = ( 30 + 5 * 2 ) years = 40 years . ( a + b + c ) , now = ( 20 x 3 ) years = 60 years . c , now = ( 60 - 40 ) years = 20 years . c , after 14 years = ( 20 + 14 ) years = 34 years . answer : b | a ) 30 , b ) 34 , c ) 40 , d ) 50 , e ) 60 | b | add(subtract(multiply(20, const_3), add(add(multiply(15, const_2), 5), 5)), 14) | multiply(n2,const_3)|multiply(n1,const_2)|add(n0,#1)|add(n0,#2)|subtract(#0,#3)|add(n3,#4) | general |
what is the ratio of 6 / 7 to the product 3 * ( 7 / 3 ) ? | "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.16 - - > x = 0.34 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.16 - - > x = 0.34 . answer : a ." | a ) 34 % , b ) 24 % , c ) 22 % , d ) 18 % , e ) 8.5 % | a | multiply(divide(subtract(multiply(const_100, divide(16, const_100)), multiply(subtract(const_100, multiply(divide(const_1, const_4), const_100)), divide(10, const_100))), multiply(divide(const_1, const_4), const_100)), const_100) | divide(n1,const_100)|divide(n0,const_100)|divide(const_1,const_4)|multiply(#0,const_100)|multiply(#2,const_100)|subtract(const_100,#4)|multiply(#1,#5)|subtract(#3,#6)|divide(#7,#4)|multiply(#8,const_100)| | gain |
if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is - . | "p ( black card ) = 1 / 2 p ( king or queen ) = 2 / 13 p ( black card then a king / queen ) = 1 / 2 * 2 / 13 = 1 / 13 the answer is b ." | a ) 1 / 52 , b ) 1 / 13 , c ) 1 / 26 , d ) 3 / 26 , e ) 17 / 26 | b | multiply(divide(add(multiply(const_3, const_4), const_1), const_52), divide(const_2, const_52)) | divide(const_2,const_52)|multiply(const_3,const_4)|add(#1,const_1)|divide(#2,const_52)|multiply(#3,#0)| | probability |
working together , jose and jane can complete an assigned task in 10 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 25 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose | "explanation : let the number of wickets taken before the last match is x . then , ( 22.2 x + 36 ) / ( x + 4 ) = 21 = > 22.2 x + 36 = 21 x + 84 = > 1.2 x = 48 = > x = 48 / 1.2 = 40 answer : d" | a ) 14 , b ) 22 , c ) 38 , d ) 40 , e ) 50 | d | divide(subtract(multiply(floor(22.2), 4), 36), subtract(22.2, floor(22.2))) | floor(n0)|multiply(n1,#0)|subtract(n0,#0)|subtract(#1,n2)|divide(#3,#2)| | general |
the true discount on a bill due 9 months hence at 16 % per annum is rs . 162 . the amount of the bill is | "explanation : a runs 1000 meters while b runs 900 meters and c runs 880 meters . therefore , b runs 900 meters while c runs 880 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 880 ) / 900 = 977.778 meters thus , b can give c ( 1000 - 977.77 ) = 22.22 meters start answer : c" | a ) 10.22 meters , b ) 11.22 meters , c ) 22.22 meters , d ) 33.22 meters , e ) none of these | c | subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 120)), subtract(multiply(const_100, const_10), 100))) | multiply(const_10,const_100)|subtract(#0,n1)|subtract(#0,n0)|multiply(#0,#1)|divide(#3,#2)|subtract(#0,#4)| | physics |
during the first two weeks of june , the total rainfall in springdale was 40 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall in inches during the second week of june ? | "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 Γ 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 450 Γ 2 / 15 ) sec = 60 sec answer : e" | a ) 30 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 60 sec | e | multiply(const_3600, divide(divide(450, const_1000), add(25, 2))) | add(n1,n2)|divide(n0,const_1000)|divide(#1,#0)|multiply(#2,const_3600)| | physics |
the edges of a cuboid are 4 cm , 5 cm and 7 cm . find the volume of the cuboid ? | you need to divide the width and length of the rectangular to equal pieces where l = w you can solve this using gcf 35 = 5 * 7 45 = 3 * 3 * 5 gcf = 5 p . s you can make squares with side of 5 answer : c | ['a ) a ) 4 inches', 'b ) b ) 6 inches', 'c ) c ) 5 inches', 'd ) d ) 8 inches', 'e ) e ) 10 inches'] | c | divide(subtract(45, 35), const_2) | subtract(n1,n0)|divide(#0,const_2) | geometry |
when n is divided by 19 , the remainder is 7 . find thee difference between previous remainder and the remainder when 18 n is divided by 9 ? | "120 - 50 = 70 50 - 25 = 25 120 - 25 = 95 the h . c . f of 25 , 70 and 95 is 5 . answer : b" | a ) 18 , b ) 5 , c ) 12 , d ) 16 , e ) none of these | b | divide(subtract(50, 25), const_2) | subtract(n1,n0)|divide(#0,const_2)| | general |
the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 2 per metre approximately | "o ( 11.6 ) + e ( β 10.4 ) + o ( β 9.2 ) + e ( 9.5 ) = 13 + ( - 10 ) + ( - 11 ) + 8 = 0 the answer is c ." | a ) - 3 , b ) - 1 , c ) 0 , d ) 1 , e ) 3 | c | add(add(add(multiply(11.6, const_1), multiply(negate(10.4), const_1)), negate(9.2)), multiply(9.5, const_1)) | multiply(n0,const_1)|multiply(n3,const_1)|negate(n1)|negate(n2)|multiply(#2,const_1)|add(#0,#4)|add(#5,#3)|add(#6,#1)| | general |
| x + 3 | β | 4 - x | = | 8 + x | how many s solutions will this equation have ? | "a perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 2205 = 3 ^ 2 * 7 ^ 7 * 5 , so if k = 5 then 2205 k = ( 3 * 7 * 5 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even ) . answer : a ." | a ) 5 , b ) 9 , c ) 15 , d ) 25 , e ) 63 | a | add(const_3, const_4) | add(const_3,const_4)| | general |
find the simple interest on $ 10000 at 7 % per annum for 12 months ? | so we can start with 2 and check whether sum of two primes is primes is even . 1 ) 2 ( 6 times ) 2 ) 2 ( 3 times ) + 3 ( 2 times ) 3 ) 2 ( 2 times ) + 3 + 5 4 ) 2 + 3 + 7 5 ) 2 + 5 + 5 6 ) 3 ( 4 times ) 7 ) 5 + 7 answer : d | a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | d | add(divide(12, const_4), const_4) | divide(n11,const_4)|add(#0,const_4) | general |
noelle walks from point a to point b at an average speed of 3 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 4 kilometers per hour ? | "speed = 144 * 5 / 18 = 40 m / sec time taken = 175 / 40 = 4.37 sec . answer : c" | a ) 2.58 sec , b ) 2.91 sec , c ) 4.37 sec , d ) 2.9 sec , e ) 1.8 sec | c | divide(175, multiply(144, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics |
niall ' s income is 60 % less than rex ' s income , and sam ' s income is 25 % less than niall ' s income . if rex gave 60 % of his income to sam and 40 % of his income to niall , niall ' s new income would be what fraction of sam ' s new income ? | "let x be the number he chose , then 5 β
x β 275 = 135 5 x = 410 x = 82 correct answer b" | a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88 | b | divide(add(135, 275), 5) | add(n1,n2)|divide(#0,n0)| | general |
find the average of all prime numbers between 1 and 5 . | "let c be the capacity of the can . ( 3 / 5 ) * ( c - 6 ) + 6 = ( 2 / 3 ) * c 9 c - 54 + 90 = 10 c c = 36 the answer is a ." | a ) 36 , b ) 34 , c ) 32 , d ) 30 , e ) 28 | a | add(add(multiply(divide(multiply(1, 6), subtract(multiply(2, 2), multiply(1, 3))), 3), 6), multiply(divide(multiply(1, 6), subtract(multiply(2, 2), multiply(1, 3))), 2)) | multiply(n2,n4)|multiply(n1,n3)|multiply(n0,n4)|subtract(#1,#2)|divide(#0,#3)|multiply(n0,#4)|multiply(n1,#4)|add(n2,#5)|add(#7,#6)| | general |
two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 60 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ? | let xx be the distance between a and b . since susan covered 80 km in 2 hours , her speed was v = 802 = 40 v = 802 = 40 km / hr . if she continued at the same speed she would be 1515 minutes late , i . e . the planned time on the road is x 40 β 1560 x 40 β 1560 hr . the rest of the distance is ( x β 80 ) ( x β 80 ) km . v = 40 + 10 = 50 v = 40 + 10 = 50 km / hr . so , she covered the distance between a and b in 2 + x β 80502 + x β 8050 hr , and it was 36 min less than planned . therefore , the planned time was 2 + x β 8050 + 36602 + x β 8050 + 3660 . when we equalize the expressions for the scheduled time , we get the equation : x 40 β 1560 = 2 + x β 8050 + 3660 x 40 β 1560 = 2 + x β 8050 + 3660 x β 1040 = 100 + x β 80 + 3050 x β 1040 = 100 + x β 80 + 3050 x β 104 = x + 505 x β 104 = x + 505 5 x β 50 = 4 x + 2005 x β 50 = 4 x + 200 x = 250 x = 250 so , the distance between cities a and b is 250 km . answer : c | a ) 223 , b ) 376 , c ) 250 , d ) 378 , e ) 271 | c | add(divide(subtract(add(subtract(divide(36, const_60), divide(80, add(divide(80, const_2), 10))), const_2), divide(15, const_60)), subtract(divide(const_1, divide(80, const_2)), divide(const_1, add(divide(80, const_2), 10)))), const_100) | divide(n3,const_60)|divide(n0,const_2)|divide(n1,const_60)|add(n2,#1)|divide(const_1,#1)|divide(n0,#3)|divide(const_1,#3)|subtract(#0,#5)|subtract(#4,#6)|add(#7,const_2)|subtract(#9,#2)|divide(#10,#8)|add(#11,const_100) | physics |
8 , 12 , 18 , 27 , 40.5 , ( . . . ) | "speed = 40 * 5 / 18 = 100 / 9 m / sec length of the train = speed * time = 100 / 9 * 9 = 100 m answer : a" | a ) 100 m , b ) 150 m , c ) 187 m , d ) 167 m , e ) 197 m | a | multiply(divide(multiply(40, const_1000), const_3600), 9) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics |
two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 25 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ? | "7 ^ 16 can be written as ( 7 ^ 4 ) ^ 4 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 4 by 100 , the reminder is 1 ^ 4 = 1 answer : d" | a ) 3 , b ) 4 , c ) 2 , d ) 1 , e ) 5 | d | subtract(divide(100, const_2), multiply(7, 7)) | divide(n2,const_2)|multiply(n0,n0)|subtract(#0,#1)| | general |
| x + 3 | β | 4 - x | = | 7 + x | how many solutions will this equation have ? | "the number of chocolate bars is equal to 17 * 25 = 425 correct answer c" | a ) 250 , b ) 350 , c ) 425 , d ) 550 , e ) 650 | c | multiply(17, 25) | multiply(n0,n1)| | general |
if 35 % of a number is 12 less than 50 % of that number , then the number is ? | explanation : = > y = x ^ 2 + 5 x + 6 = > y = ( x + 2 ) ( x + 3 ) = > x = - 2 , x = - 3 product x = ( - 2 ) ( - 3 ) = 6 answer option 6 answer : d | a ) 12 , b ) 18 , c ) 15 , d ) 6 , e ) 9 | d | divide(6, const_1) | divide(n2,const_1) | general |
in the manufacture of a certain product , 9 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ? | "u / i = 6 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 30 : 18 : 2 i . e . u : b = 30 : 2 answer : option b" | a ) 5 : 1 , b ) 30 : 2 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2 | b | divide(multiply(6, 5), multiply(1, 2)) | multiply(n0,n2)|multiply(n1,n3)|divide(#0,#1)| | other |
when a certain number x is divided by 54 , the remainder is 22 . what is the remainder when x is divided by 18 ? | when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 3 * 15 / 60 = 15 / 20 miles and the man walks the distance mm , which is 3 * 9 / 60 = 9 / 20 mile . the difference of 15 / 20 - 9 / 20 = 3 / 10 miles ( mw ) will be covered by the man in ( 3 / 10 ) / 9 = 1 / 30 of an hour , which is 2 minutes . answer b . | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | b | multiply(const_60, divide(multiply(divide(3, const_60), subtract(15, 9)), 9)) | divide(n2,const_60)|subtract(n1,n0)|multiply(#0,#1)|divide(#2,n0)|multiply(#3,const_60) | physics |
each machine of type a has 3 steel parts and 3 chrome parts . each machine of type b has 6 steel parts and 5 chrome parts . if a certain group of type a and type b machines has a total of 60 steel parts and 44 chrome parts , how many machines are in the group | "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 80 % of republicans ( which is ( 60 * 0.8 ) = 48 ) and 20 % of democrats ( 40 * 0.2 = 8 ) voted for candidate x , means that out of total of 100 voters ; 56 ( 48 + 8 ) voters voted for candidate x and 44 voted for candidate y . thus we can infer that candidate x is expected to win the election by 12 ( 56 - 44 ) votes . therefore candidate x is expected to win the election by ( 12 / 100 ) votes which is equivalent to 12 % . i think the answer is e ." | a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 12 % | e | multiply(divide(subtract(add(multiply(divide(20, const_100), 2), multiply(divide(80, const_100), 3)), add(subtract(3, multiply(divide(80, const_100), 3)), subtract(2, multiply(divide(20, const_100), 2)))), add(3, 2)), const_100) | add(n0,n1)|divide(n3,const_100)|divide(n2,const_100)|multiply(n1,#1)|multiply(n0,#2)|add(#3,#4)|subtract(n0,#4)|subtract(n1,#3)|add(#6,#7)|subtract(#5,#8)|divide(#9,#0)|multiply(#10,const_100)| | other |
a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 35 % lemonade syrup ? | "let us suppose there are 100 people . 40 % of them donated $ 16000 ( 400 * 40 ) $ 16000 is 50 % of total amount . so total amount = 16000 * 100 / 50 remaining amount is 50 % of total amount . 50 % of total amount = 16000 * ( 100 / 50 ) * ( 50 / 100 ) = 16000 this amount has to be divided by 50 ( remaining people are 50 ) so per head amount is 16000 / 50 = 320 answer : c" | a ) $ 400 , b ) $ 177.78 , c ) $ 320 , d ) $ 277 , e ) $ 200 | c | divide(multiply(divide(multiply(divide(40, const_100), 400), divide(50, const_100)), divide(40, const_100)), divide(50, const_100)) | divide(n2,const_100)|divide(n0,const_100)|multiply(n1,#0)|divide(#2,#1)|multiply(#3,#0)|divide(#4,#1)| | general |
cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost q is what percent of the original cost ? | "though there might be some technicalities concerning the termnearest ( as 9.5 is equidistant from both 9 and 10 ) the answer still should be : 9.5 ^ 2 = 90.25 . answer : e" | a ) 96.25 sq cm , b ) 98.25 sq cm , c ) 92.25 sq cm , d ) 100.25 sq cm , e ) 90.25 sq cm | e | power(subtract(subtract(10, const_0_25), const_0_25), const_2) | subtract(n0,const_0_25)|subtract(#0,const_0_25)|power(#1,const_2)| | geometry |
a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 4 inches wide on each side , the total area would have been ( m + 108 ) square inches . what is the perimeter of the photograph , in inches ? | "m s / w has 100 line of code n s / w has = 100 + 100 * 1 / 2 = 150 line of code p s / w 5 % more n ' code 150 + 7.5 = 157.5 or 158 line of code answer : e" | a ) 106 , b ) 107 , c ) 108 , d ) 109 , e ) 158 | e | add(100, divide(100, 2)) | divide(n3,n2)|add(n3,#0)| | general |
a can do a piece of work in 6 hours ; b and c together can do it in 4 hours , which a and c together can do it in 3 hours . how long will b alone take to do it ? | "explanation : each row contains 15 plants . there are 14 gapes between the two corner trees ( 14 x 2 ) metres and 1 metre on each side is left . therefore length = ( 28 + 2 ) m = 30 m . answer : b" | a ) 20 m , b ) 30 m , c ) 24 m , d ) 26 m , e ) 28 m | b | add(add(multiply(subtract(15, const_1), 2), divide(10, 2)), divide(10, 2)) | divide(n0,n2)|subtract(n1,const_1)|multiply(n2,#1)|add(#0,#2)|add(#3,#0)| | physics |
in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 170 m . then , a wins by : | "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 50.50 = ( 10 / 100 ) * 50.50 = $ 5.05 total spent 50.50 + 5.05 = $ 55.55 correct answer d" | a ) $ 30.60 , b ) $ 60.60 , c ) $ 70.60 , d ) $ 55.55 , e ) $ 50.60 | d | add(50.50, divide(multiply(50.50, 10), const_100)) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)| | gain |
in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the ` ` sport ' ' formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the ` ` sport ' ' formulation contains 3 ounces of corn syrup , how many ounces of water does it contain ? | "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 240 / 9 = 500 / 9 x = 260 ans is 260 m answer : a" | a ) 260 m , b ) 220 m , c ) 230 m , d ) 240 m , e ) 250 m | a | subtract(multiply(9, multiply(add(120, 80), const_0_2778)), 240) | add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0)| | physics |
two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 48 kmph respectively . in how much time will they cross each other , if they are running in the same direction ? | answer a . we are told that 10 % of all imported widgets are made of brass and of those , 20 % are green and 40 % are red . since we know that there are only three colors , the remaining 40 % must be blue . 40 % blue of 10 % brass widgets leads to 4 % blue brass widgets out of the total 10,550 widgets . 12,000 / 100 * 4 = 480 . answer b . | a ) 420 , b ) 480 , c ) 1050 , d ) 1680 , e ) 2100 | b | multiply(multiply(multiply(multiply(divide(10, const_100), divide(40, const_100)), divide(add(10, const_2), 10)), const_100), const_100) | add(n1,const_2)|divide(n1,const_100)|divide(n3,const_100)|divide(#0,n1)|multiply(#1,#2)|multiply(#3,#4)|multiply(#5,const_100)|multiply(#6,const_100) | gain |
a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 11,900 sedans in anytown , how many motorcycles are there ? | here when he step down 26 steps he has 30 seconds for remaining steps . if he step down 34 stairs he has only 18 sec . 30 - 18 = 12 12 secs for 8 steps . . 18 secs for 12 steps . 12 + 34 = 46 so ans is 46 . . answer : b | a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9 | b | subtract(add(multiply(divide(subtract(34, 26), subtract(30, 18)), 30), 26), multiply(const_4, const_10)) | multiply(const_10,const_4)|subtract(n2,n0)|subtract(n1,n3)|divide(#1,#2)|multiply(n1,#3)|add(n0,#4)|subtract(#5,#0) | physics |
when y is divided by 288 , the remainder is 44 . what is the remainder when the same y is divided by 24 ? | "the volume of the mixture be x + y . 0.3 x + 0.4 y = 0.36 ( x + y ) x = 2 y / 3 x / ( x + y ) = ( 2 y / 3 ) / ( 5 y / 3 ) = 2 / 5 = 40 % . the answer is c ." | a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 % | c | multiply(divide(divide(subtract(40, 36), subtract(36, 30)), add(divide(subtract(40, 36), subtract(36, 30)), const_1)), const_100) | subtract(n2,n4)|subtract(n4,n0)|divide(#0,#1)|add(#2,const_1)|divide(#2,#3)|multiply(#4,const_100)| | gain |
a sum of 13,400 amounts to 14,400 in 2 years at the rate of simple interest . what is the rate of interest ? | "let the fixed charge of jim β s taxi service = 2.45 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.45 + ( 3.6 / . 4 ) * . 35 = 2.45 + 9 * . 35 = 5.6 $ answer e" | a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.6 | e | add(2.45, multiply(0.35, divide(3.6, divide(2, 5)))) | divide(n2,n3)|divide(n4,#0)|multiply(n1,#1)|add(n0,#2)| | general |
a can complete a work in 15 days and b can do the same work in 9 days . if a after doing 5 days , leaves the work , find in how many days b will do the remaining work ? | let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.2 x red + yellow = 0.45 x red = 0.225 x , since red = yellow . the answer is c . | a ) 12.5 % , b ) 16.7 % , c ) 22.5 % , d ) 27.5 % , e ) 33.3 % | c | multiply(divide(divide(subtract(24, add(divide(divide(const_100, add(const_2, const_3)), const_2), divide(divide(divide(const_100, add(const_2, const_3)), const_2), const_2))), const_2), divide(const_100, add(const_2, const_3))), const_100) | add(const_2,const_3)|divide(const_100,#0)|divide(#1,const_2)|divide(#2,const_2)|add(#2,#3)|subtract(n0,#4)|divide(#5,const_2)|divide(#6,#1)|multiply(#7,const_100) | general |
if the selling price of 100 articles is equal to the cost price of 63 articles , then the loss or gain percent is : | "( c . p . of 9 balls ) - ( s . p . of 9 balls ) = ( c . p . of 5 balls ) c . p . of 4 balls = s . p . of 9 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 4 = rs . 180 . answer : option e" | a ) s . 145 , b ) s . 150 , c ) s . 155 , d ) s . 160 , e ) s . 180 | e | divide(720, subtract(9, 5)) | subtract(n0,n2)|divide(n1,#0)| | gain |
carol spends 1 / 3 of her savings on a stereo and 1 / 3 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ? | "cost price = 630 / 90 x 100 = 700 to gain 10 % = 700 x 10 / 100 = 70 sp = cp + gain = 700 + 70 = 770 answer : d" | a ) 430 , b ) 450 , c ) 550 , d ) 770 , e ) 660 | d | add(divide(630, subtract(const_1, divide(10, const_100))), multiply(divide(630, subtract(const_1, divide(10, const_100))), divide(10, const_100))) | divide(n1,const_100)|divide(n2,const_100)|subtract(const_1,#0)|divide(n0,#2)|multiply(#3,#1)|add(#3,#4)| | gain |
on a certain transatlantic crossing , 20 percent of a ship β s passengers held round - trip tickets and also took their cars abroad the ship . if 50 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship β s passengers held round - trip tickets ? | "c = 1 / 5 β 1 / 11 = 6 / 55 = > 9.2 days answer : d" | a ) 15.5 days , b ) 19.5 days , c ) 17.5 days , d ) 9.2 days , e ) 18.5 days | d | inverse(subtract(5, divide(5, 11))) | divide(n1,n0)|subtract(n1,#0)|inverse(#1)| | physics |
a bakery has 6 employees . it pays annual salaries of $ 19000 to each of 2 employees , $ 21000 to 1 employee , and $ 22000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ? | "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 310 * 3 / 55 ] sec = 17 sec answer : d" | a ) 4 , b ) 6 , c ) 5 , d ) 17 , e ) 13 | d | multiply(const_3600, divide(divide(310, const_1000), add(60, 6))) | add(n1,n2)|divide(n0,const_1000)|divide(#1,#0)|multiply(#2,const_3600)| | physics |
one fourth of a solution that was 10 % sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ? | start with the prime factorization : 210 = 2 * 3 * 5 * 7 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 , 1 } plus 1 to each = { 2 , 2 , 2 } product = 2 * 2 * 2 = 8 therefore , there are 8 odd factors of 210 . in case you are curious , they are { 1 , 3 , 5 , 7 , 15 , 21 , 35 , and 105 } answer : e . | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8 | e | add(add(add(const_4, const_2), const_1), const_1) | add(const_2,const_4)|add(#0,const_1)|add(#1,const_1) | other |
the general hospital is comprised of , 3 / 5 pediatricians , 1 / 4 surgeons , and the rest are gp doctors . if 1 / 4 of the surgeons are heart surgeons , and the hospital doubles the number of gp doctors , what proportion of the hospital are now heart surgeons ? | "7 regular days - - > sales = 7 * 32 * x = 224 x ; 3 hot days - - > sales = 3 * 32 * ( 1.25 x ) = 120 x ; total sales = 224 x + 120 x = 344 x . total cost = 10 * 32 * 0.75 = 240 . profit = 344 x - 240 = 350 - - > x = 1.715 . 1.25 x = ~ 2.14 . answer : c ." | a ) $ 1.50 , b ) $ 1.88 , c ) $ 2.14 , d ) $ 2.50 , e ) $ 3.25 | c | multiply(divide(add(multiply(multiply(32, divide(75, const_100)), multiply(add(const_4, 1), const_2)), 350), add(multiply(subtract(multiply(add(const_4, 1), const_2), 3), 32), multiply(multiply(divide(add(const_100, 25), const_100), 3), 32))), divide(add(const_100, 25), const_100)) | add(n5,const_4)|add(n1,const_100)|divide(n2,const_100)|divide(#1,const_100)|multiply(n3,#2)|multiply(#0,const_2)|multiply(#4,#5)|multiply(n4,#3)|subtract(#5,n4)|add(n0,#6)|multiply(n3,#8)|multiply(n3,#7)|add(#10,#11)|divide(#9,#12)|multiply(#13,#3)| | gain |
a man has some hens and cows . if the number of heads be 42 and the number of feet equals 124 , then the number of hens will be | "2 ^ 8 - 1 = ( 2 ^ 4 - 1 ) ( 2 ^ 4 + 1 ) = 15 * 17 the answer is c ." | a ) 11 , b ) 13 , c ) 17 , d ) 19 , e ) 23 | c | floor(divide(2, divide(8, const_2))) | divide(n1,const_2)|divide(n0,#0)|floor(#1)| | general |
pipe p can drain the liquid from a tank in 2 / 4 the time that it takes pipe q to drain it and in 2 / 3 the time that it takes pipe r to do it . if all 3 pipes operating simultaneously but independently are used to drain liquid from the tank , then pipe q drains what portion of the liquid from the tank ? | "given 2 x = 3 y = 5 z x + y + z in terms of x = x + ( 2 x / 3 ) + ( 2 x / 5 ) = 31 x / 15 now checking with each of the answers and see which value gives a minimum integer value . a x = 15 / 31 * 40 , not an integer b , c , d can be ruled out similarly . e is minimum value as x = 15 * 31 / 31 = 15 answer is e" | a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 31 | e | add(subtract(divide(multiply(multiply(2, 3), 4), 2), divide(multiply(multiply(2, 3), 4), 3)), divide(multiply(multiply(2, 3), 4), 4)) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,n2)|divide(#1,n0)|divide(#1,n1)|subtract(#3,#4)|add(#2,#5)| | general |
when 1 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ? | "we have the rectangle with dimensions 9 * 7 ( 9 horizontal dots and 7 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 7 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 6 c 1 , ( 7 - 1 = 6 as 1 vertical dot is already occupied by a ) . 9 c 1 * 7 c 1 * 8 c 1 * 6 c 1 = 3024 answer : d ." | a ) 54 , b ) 432 , c ) 2,160 , d ) 3024 , e ) 148,824 | d | multiply(multiply(7, subtract(7, const_1)), multiply(9, 7)) | multiply(n0,n3)|subtract(n0,const_1)|multiply(n0,#1)|multiply(#2,#0)| | geometry |
a tank is filled by 3 pipes a , b , c in 7 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ? | c $ 90 let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 . | a ) 50 , b ) 60 , c ) 90 , d ) 48 , e ) 67 | c | add(divide(multiply(480, 10), const_60), 10) | multiply(n0,n2)|divide(#0,const_60)|add(n2,#1) | general |
the angle between the minute hand and the hour hand of a clock when the time is 10.30 , is | "let n = 6 ( leaves a remainder of 6 when divided by 48 ) 4 n = 4 ( 6 ) = 24 , which leaves a remainder of 0 when divided by 8 . answer a" | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | subtract(6, reminder(4, 8)) | reminder(n2,n3)|subtract(n1,#0)| | general |
a company pays 20.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ? | if sum of the digits is divisible by 3 , the number is divisible by 3 . therefore , required number of non - negative integers is equal to count of numbers less than 10000 which are divisible by 3 . such numbers are ( 3 , 6 , 9 , . . . , 9999 ) ( arithmetic progression with first term = 3 , last term = 9999 , common difference = 3 ) . count of such numbers = 9999 3 = 3333 99993 = 3333 but zero is also divisible by 3 . this makes our total count 3334 d | a ) 2468 , b ) 2789 , c ) 2987 , d ) 3334 , e ) 3568 | d | add(floor(divide(10000, 3)), const_1) | divide(n0,n1)|floor(#0)|add(#1,const_1) | general |
a block of wood has dimensions 10 cm x 10 cm x 90 cm . the block is painted red and then cut evenly at the 45 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ? | "the ratio of their working rates = 1 / 7 : 1 / 14 : 1 / 21 = 6 : 3 : 2 . since , they work together , the share of c = 2 / 11 * 242 = rs . 44 \ answer : b" | a ) 33 , b ) 44 , c ) 55 , d ) 77 , e ) 99 | b | multiply(242, divide(inverse(14), add(inverse(21), add(inverse(7), inverse(14))))) | inverse(n1)|inverse(n0)|inverse(n2)|add(#1,#0)|add(#3,#2)|divide(#0,#4)|multiply(n3,#5)| | physics |
a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 30 . find the profit percentage ? | "p = 4320 r = 20 % required population of town = p / ( 1 + r / 100 ) ^ t = 4320 / ( 1 + 20 / 100 ) ^ 2 = 4320 / ( 6 / 5 ) ^ 2 = 3000 ( approximately ) answer is d" | a ) 2500 , b ) 2100 , c ) 3500 , d ) 3000 , e ) 2050 | d | add(4320, divide(multiply(4320, 20), const_100)) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)| | gain |
if 7 a - 3 b = 10 b + 50 = - 12 b - 2 a , what is the value of 9 a + 9 b ? | "12 m + 16 b - - - - - 7 days 13 m + 24 b - - - - - - - 4 days 84 m + 112 b = 52 m + 96 b 32 m = 16 b = > 2 m = b m : b = 1 : 2 answer : b" | a ) 1 : 4 , b ) 1 : 2 , c ) 1 : 3 , d ) 2 : 1 , e ) 4 : 1 | b | divide(subtract(multiply(4, 24), multiply(7, 16)), subtract(multiply(7, 12), multiply(4, 13))) | multiply(n4,n5)|multiply(n1,n2)|multiply(n0,n2)|multiply(n3,n5)|subtract(#0,#1)|subtract(#2,#3)|divide(#4,#5)| | physics |
an angry arjun carried some arrows for fighting with bheeshm . with half the arrows , he cut down the arrows thrown by bheeshm on him and with 6 other arrows he killed the chariot driver of bheeshm . with one arrow each he knocked down respectively the chariot , the flag and the bow of bheeshm . finally , with one more than 4 times the square root of arrows he laid bheeshm unconscious on an arrow bed . find the total number of arrows arjun had . | "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 6 days = 6 ( 1 / 18 ) = 1 / 3 . answer c" | a ) 2 / 5 , b ) 1 / 6 , c ) 1 / 3 , d ) 1 / 9 , e ) 2 / 6 | c | multiply(6, add(divide(const_1, 30), divide(const_1, 45))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)| | physics |
if the sides of a cube are in the ratio 9 : 5 . what is the ratio of their diagonals ? | "number of boxes = total volume / volume of one box = 432,000 / ( 8 * 10 * 12 ) = 450 one box costs 7.50 , so 450 box will cost = 450 * 7.5 = 3375 e is the answer" | a ) $ 960 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 3,375 | e | divide(multiply(divide(multiply(add(add(multiply(const_3, const_100), multiply(8, 10)), const_4), const_1000), multiply(multiply(8, 10), 12)), 7.50), const_1000) | multiply(const_100,const_3)|multiply(n0,n1)|multiply(n0,n1)|add(#0,#1)|multiply(n2,#2)|add(#3,const_4)|multiply(#5,const_1000)|divide(#6,#4)|multiply(n3,#7)|divide(#8,const_1000)| | general |
marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 35 % . what percent of the projected revenue was the actual revenue ? | "solution : let the arrangement be , b g b g b g b g 4 boys can be seated in 4 ! ways . girl can be seated in 4 ! ways . required number of ways , = 4 ! * 4 ! = 576 . answer : option d" | a ) 144 , b ) 288 , c ) 12 , d ) 576 , e ) none | d | multiply(factorial(4), factorial(4)) | factorial(n0)|factorial(n1)|multiply(#0,#1)| | probability |
the average price of 3 items of furniture is rs . 15000 . if their prices are in the ratio 2 : 4 : 8 , the price of the cheapest item is ? | "rs = 5 ΒΎ - 4 Β½ = 1 ΒΌ t = 4 Β½ h . d = 5 / 4 * 9 / 2 = 45 / 8 = 5 5 / 8 km answer : c" | a ) 7 km , b ) 6 km , c ) 5 5 / 8 km , d ) 9 km , e ) 5 km | c | add(multiply(add(4, divide(const_1, const_2)), subtract(add(5, divide(const_3, 4)), add(4, divide(const_1, const_2)))), const_2) | divide(const_1,const_2)|divide(const_3,n0)|add(n2,#0)|add(n1,#1)|add(n0,#0)|subtract(#3,#4)|multiply(#2,#5)|add(#6,const_2)| | physics |
what is the least value of x . so that 22 x 57 is divisible by 3 . | explanation : kavi ' s monthly income = rs . 19,000 he spends 50 % on food . the total money spent on food = 50 / 100 * 19000 = rs . 9500 now , his monthly remaining income = rs . 19000 β rs . 9500 = rs . 9500 out of rs . 9500 , he saves 40 % . amount saved = 40 / 100 * 9500 = rs . 3800 answer : d | a ) rs . 2000 , b ) rs . 600 , c ) rs . 8000 , d ) rs . 3800 , e ) rs . 1200 | d | divide(divide(multiply(divide(multiply(19000, 50), const_100), 80), const_100), const_2) | multiply(n0,n2)|divide(#0,const_100)|multiply(n1,#1)|divide(#2,const_100)|divide(#3,const_2) | gain |
for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 5 of whom are females , by how much does the index for the females exceed the index for the males in the group ? | "us = 40 ds = 52 m = ( 40 + 52 ) / 2 = 46 answer : d" | a ) 27 , b ) 40 , c ) 42 , d ) 46 , e ) 24 | d | divide(add(40, 52), const_2) | add(n0,n1)|divide(#0,const_2)| | physics |
a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 25 % of the original number . what percent of the red candies remain ? | "this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 10 x 20 / ( 10 + 20 ) = 200 / 30 = 6.666 days answer : c" | a ) a ) 5.333 , b ) b ) 6 , c ) c ) 6.666 , d ) d ) 8.333 , e ) e ) 9 | c | divide(const_1, add(divide(const_1, 10), divide(const_1, 20))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2)| | physics |
what is the area inscribed by the lines y = 2 , x = 2 , y = 10 - x on an xy - coordinate plane ? | "to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 100 tons will be 200,000 pounds from the answer choices : let max number of vehicles be 120 total weight will be = 120 * 1600 = 192000 pounds , which is lesser than the maximum weight allowed . ans : e" | a ) 110 , b ) 128 , c ) 115 , d ) 130 , e ) 120 | e | divide(multiply(multiply(100, const_2), const_1000), add(add(add(add(add(add(const_1000, const_100), const_100), const_100), const_100), const_100), const_100)) | add(const_100,const_1000)|multiply(n0,const_2)|add(#0,const_100)|multiply(#1,const_1000)|add(#2,const_100)|add(#4,const_100)|add(#5,const_100)|add(#6,const_100)|divide(#3,#7)| | general |
a rower can row 5 km / h in still water . when the river is running at 2 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ? | "sol . s . i . = rs . [ 10 * 3 / 100 * 4 ] = rs . 1.20 answer a" | a ) 1.2 , b ) 1.4 , c ) 2.25 , d ) 3.21 , e ) none | a | divide(multiply(multiply(10, 4), 3), const_100) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,const_100)| | gain |
a student got 72 % in math and 82 % in history . to get an overall average of 75 % , how much should the student get in the third subject ? | "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 48 * 10 = 480 m . the length of the faster train = 480 m . answer : e" | a ) 270 , b ) 288 , c ) 266 , d ) 299 , e ) 480 | e | multiply(divide(subtract(72, 36), const_3_6), 48) | subtract(n0,n1)|divide(#0,const_3_6)|multiply(n2,#1)| | physics |
a positive number x is multiplied by 5 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ? | "let x be the original number of each color . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.25 x red + yellow = 0.5 x red = 0.25 x , since red = yellow . the answer is c ." | a ) 10 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 40 % | c | multiply(divide(divide(subtract(25, add(divide(divide(const_100, add(const_2, const_3)), const_2), divide(divide(divide(const_100, add(const_2, const_3)), const_2), const_2))), const_2), divide(const_100, add(const_2, const_3))), const_100) | add(const_2,const_3)|divide(const_100,#0)|divide(#1,const_2)|divide(#2,const_2)|add(#2,#3)|subtract(n0,#4)|divide(#5,const_2)|divide(#6,#1)|multiply(#7,const_100)| | general |
a fruit seller had some oranges . he sells 10 % oranges and still has 360 oranges . how many oranges he had originally ? | "the units digit of 63 ^ 4 is the units digit of 3 ^ 4 which is 1 . the units digit of 41 ^ 7 is the units digit of 1 ^ 7 which is 1 . the units digit of 99 ^ 9 is the units digit of 9 ^ 9 which is 9 . note the pattern : 9 ^ 1 = 9 , 9 ^ 2 = 81 , 9 ^ 3 = 729 , . . . the units digit alternates between 9 and 1 . the units digit of 1 * 1 * 9 is 9 . the answer is e ." | a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9 | e | divide(add(multiply(factorial(63), factorial(4)), multiply(factorial(63), factorial(7))), 63) | factorial(n0)|factorial(n1)|factorial(n3)|multiply(#0,#1)|multiply(#0,#2)|add(#3,#4)|divide(#5,n0)| | general |
a car is running at a speed of 110 kmph . what distance will it cover in 9 sec ? | answer : c | a ) - 32 , b ) - 30 , c ) 34 , d ) - 24 , e ) - 10 | c | add(multiply(negate(4), negate(8)), 2) | negate(n0)|negate(n1)|multiply(#0,#1)|add(n4,#2) | general |
find the length of the wire required to go 12 times round a square field containing 104976 m 2 . | "explanation : required number of students = h . c . f of 1234 and 874 = 2 . answer : b" | a ) 91 , b ) 2 , c ) 1001 , d ) 1911 , e ) none of these | b | gcd(1234, 874) | gcd(n0,n1)| | general |
if ( 4 - x ) / ( 3 + x ) = x , what is the value of x ^ 2 + 4 x - 4 ? | net speed = 3 + 2 = 5 m / sec distance = 100 m time = 100 / 5 = 20 sec answer d | a ) 30 , b ) 10 , c ) 15 , d ) 20 , e ) 25 | d | divide(100, add(3, 2)) | add(n0,n1)|divide(n2,#0) | physics |
jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 3.5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill ) | explanation : ds = 12 us = 8 s = ? s = ( 12 - 8 ) / 2 = 2 kmph answer : a | a ) 2 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 9 kmph | a | divide(subtract(12, 8), const_2) | subtract(n0,n1)|divide(#0,const_2) | gain |
the bus fare for two persons for travelling between agra and aligarh id 4 - thirds the train fare between the same places for one person . the total fare paid by 6 persons travelling by bus and 8 persons travelling by train between the two places is rs . 1512 . find the train fare between the two places for one person ? | "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 60,000 i . e . rs . 30,000 answer : c" | a ) rs . 27,000 , b ) rs . 24,000 , c ) rs . 30,000 , d ) rs . 36,000 , e ) none of these | c | multiply(add(multiply(multiply(multiply(const_4, 2), multiply(add(2, const_3), 2)), const_100), multiply(multiply(add(2, const_3), const_100), const_100)), divide(divide(multiply(add(2, const_3), 2), 2), multiply(const_4, const_3))) | add(n1,const_3)|multiply(n1,const_4)|multiply(const_3,const_4)|multiply(#0,n1)|multiply(#0,const_100)|divide(#3,n1)|multiply(#1,#3)|multiply(#4,const_100)|divide(#5,#2)|multiply(#6,const_100)|add(#9,#7)|multiply(#10,#8)| | gain |
find the ratio in which rice at rs . 7.30 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg | "a + b = 240 b + c = 300 a - c = - 60 . imo option a ." | a ) β 60 , b ) β 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given | a | subtract(multiply(150, const_2), multiply(120, const_2)) | multiply(n1,const_2)|multiply(n0,const_2)|subtract(#0,#1)| | general |
the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 10 students is 16 years . the age of the 15 th student is | "25 % of 2 litres = 0.5 litres 30 % of 6 litres = 1.8 litres therefore , total quantity of alcohol is 2.3 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 23 % answer : a" | a ) 23 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % . | a | multiply(divide(add(multiply(divide(25, const_100), 2), multiply(divide(30, const_100), 6)), 10), const_100) | divide(n1,const_100)|divide(n3,const_100)|multiply(n0,#0)|multiply(n2,#1)|add(#2,#3)|divide(#4,n5)|multiply(#5,const_100)| | general |
boy sells a book for rs . 630 he gets a loss of 10 % , to gain 10 % , what should be the sp ? | "assume the current age = a a - x / 4 = 14 ( i ) a + x / 4 = 4 x or a = 15 x / 4 ( ii ) putting the value of a from ( ii ) in ( i ) 15 x / 4 - x / 4 = 14 or 14 x / 4 = 14 therefore x = 4 and a = 15 3 x years from now , age will be 15 + 3 * 4 = 27 option e" | a ) 32 , b ) 35 , c ) 30 , d ) 40 , e ) 27 | e | subtract(multiply(multiply(4, 3), 4), divide(subtract(14, const_1), const_2)) | multiply(n0,n4)|subtract(n1,const_1)|divide(#1,const_2)|multiply(n0,#0)|subtract(#3,#2)| | general |
sum of two numbers prime to each other is 12 and their l . c . m . is 35 . what are the numbers ? | "total number of ways to choose 2 out of 6 workers = 6 ! / 2 ! 4 ! = 15 number of ways to choose both jack and jill = 1 probability = 1 / 15 c should be the answer" | a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 15 , d ) 3 / 8 , e ) 2 / 3 | c | inverse(divide(factorial(6), multiply(factorial(2), factorial(4)))) | factorial(n2)|factorial(n1)|factorial(n0)|multiply(#1,#2)|divide(#0,#3)|inverse(#4)| | physics |
list a consists of 12 consecutive integers . if - 4 is the least integer in list a , what is the range of positive integers in list a ? | "find the product of the two increases : ( 1.4 ) * ( 1.35 ) which is 1.89 and a 89 % increase . d" | a ) 65 % , b ) 70 % , c ) 75 % , d ) 89 % , e ) 95 % | d | multiply(subtract(divide(multiply(multiply(const_100, add(const_1, divide(40, const_100))), add(const_1, divide(35, const_100))), const_100), const_1), const_100) | divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(#3,const_100)|multiply(#2,#4)|divide(#5,const_100)|subtract(#6,const_1)|multiply(#7,const_100)| | gain |
if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 30 % of m is equal to what percent of 200 % of j ? | "if we divide 9879 by 10 remainder is 9 10 - 9 = 1 answer : c" | a ) 3 , b ) 4 , c ) 1 , d ) 2 , e ) 6 | c | subtract(multiply(add(multiply(const_4, const_10), const_2), 10), 9879) | multiply(const_10,const_4)|add(#0,const_2)|multiply(n1,#1)|subtract(#2,n0)| | general |
27 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ? | "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 150 then y = 450 answer : d" | a ) 250 / 3 , b ) 500 / 3 , c ) 400 , d ) 450 , e ) 600 | d | multiply(divide(subtract(25, 10), subtract(30, 25)), 150) | subtract(n3,n0)|subtract(n1,n3)|divide(#0,#1)|multiply(n2,#2)| | general |
a bookseller sells his books at a 20 % markup in price . if he sells a book for $ 24.00 , how much did he pay for it ? | "750 - - - - 180 100 - - - - ? = > 44 % answer : b" | a ) 22 , b ) 44 , c ) 99 , d ) 88 , e ) 11 | b | multiply(divide(subtract(1080, 750), 750), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
a box measuring 49 inches long by 21 inches wide by 14 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ? | "explanation : 6500 : 1300 : 7800 5 : 1 : 6 1 / 12 * 11700 = 975 answer : d" | a ) 1300 , b ) 3877 , c ) 1170 , d ) 975 , e ) 7800 | d | multiply(divide(6500, add(add(6500, 1300), 7800)), 11700) | add(n0,n1)|add(n2,#0)|divide(n0,#1)|multiply(n3,#2)| | gain |
reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 300 as interest at the end of the loan period , what was the rate of interest ? | "total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 65 = 975 so , the score of the person who left is 25 ( 1000 - 975 ) answer will be ( b )" | a ) a ) 10 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70 | b | subtract(multiply(16, 62.5), multiply(subtract(16, const_1), 65.0)) | multiply(n0,n1)|subtract(n0,const_1)|multiply(n2,#1)|subtract(#0,#2)| | general |
4242 Γ 9999 = ? | "explanation : = ( 35 / 100 ) * 450 + ( 45 / 100 ) * 350 = 315 option c" | a ) 232 , b ) 242 , c ) 315 , d ) 262 , e ) 272 | c | divide(35, divide(450, 35)) | divide(n1,n0)|divide(n0,#0)| | gain |
rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 2 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ? | "when positive integer x is divided by positive integer y , the remainder is 8 - - > x = qy + 8 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 8 - - > y = 66.7 . answer : c ." | a ) 96 , b ) 75 , c ) 66.7 , d ) 25 , e ) 12 | c | divide(8, subtract(96.12, floor(96.12))) | floor(n1)|subtract(n1,#0)|divide(n0,#1)| | general |
a box contains 8 pairs of shoes ( 16 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ? | a 10 kmph time left = 10 - 3 / 5 * 10 = 4 hr 10 km / h speed = 40 km / 4 hr = 10 kmph | a ) 10 kmph , b ) 20 kmph , c ) 30 kmph , d ) 40 kmph , e ) 50 kmph | a | divide(divide(80, const_2), subtract(10, multiply(divide(10, 5), 3))) | divide(n0,const_2)|divide(n1,n3)|multiply(n2,#1)|subtract(n1,#2)|divide(#0,#3) | physics |