Cheukting/mathqa huggingface dataset:
Question (gain): an error 1 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ?
Options: a ) 4.05 % , b ) 4.02 % , c ) 4 % , d ) 3 % , e ) 2.01 %
Rationale: "percentage error in calculated area = ( 1 + 1 + ( 1 ã — 1 ) / 100 ) % = 2.01 % answer : e"
Answer: e
Question (general): a survey of n people in the town of eros found that 50 % of them preferred brand a . another surveyof 100 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "50 % of n people from eros prefer brand a . 50 % of n is 50 / 100 x n = n / 2 . 60 % of 100 people from angie prefer brand a . 60 % of 100 is 60 / 100 x 100 = 60 . of the total n + 100 people surveyed , n / 2 + 60 prefer brand a . given that this is 55 % , we have ( n / 2 + 60 ) / ( n + 100 ) x 100 = 55 solving the equation ( n / 2 + 60 ) / ( n + 100 ) x 100 = 55 ( n / 2 + 60 ) = 55 / 100 x ( n + 100 ) ( n / 2 + 60 ) = 11 / 20 n + 55 0 = 11 n / 20 – n / 2 + 55 - 60 now subtracting n / 2 and 60 from both sides 0 = n / 20 - 5 adding 5 on both sides 5 = n / 20 n = 100 hence , the total number of people surveyed is n + 100 = 100 + 100 = 200 . answer : d"
Answer: d
Question (general): 325.124 x 12.98 ã · 3.001 + 21.21 = ?
Options: a ) 1430.08 , b ) 1420.06 , c ) 781.189 , d ) 656.112 , e ) 456.512
Rationale: "explanation : ? = 325.124 x 12.98 ã · 3.001 + 21.21 = ? â ‰ ˆ ( 325.124 x 13 / 3 ) + 21.21 â ‰ ˆ 1408.87 + 21.21 â ‰ ˆ 1430.080 answer : option a"
Answer: a
Question (general): gold is 19 times as heavy as water and copper is 9 times heavy . in what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water ?
Options: a ) 2 : 3 , b ) 3 : 2 , c ) 1 : 3 , d ) 2 : 1 , e ) none of these
Rationale: "? required ratio = 6 ? 4 = 3 : 2 answer b"
Answer: b
Question (geometry): in triangle pqr , the angle q = 90 degree , pq = 7 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz
Options: a ) 5.6 cm
b ) 2.4 cm
c ) 4.8 cm
d ) 2.16 cm
e ) 3.2 cm
Rationale: look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 7 = 8 : 10 - - > qy = 5.6 . answer : a .
Answer: a
Question (other): in a family 15 people eat only vegetarian , 8 people eat only non veg . , 11 people eat both veg and non veg . . how many people eat veg in the family ?
Options: a ) 20 , b ) 11 , c ) 23 , d ) 26 , e ) 21
Rationale: "total people eat veg = only veg + both veg and non veg total = 15 + 11 = 26 answer = d"
Answer: d
Question (physics): two trains a and b are 125 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 11 s , c ) 4 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 125 + 150 = 275 m . time taken = 275 / 25 = 11 s . correct answer b ."
Answer: b
Question (physics): together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours t would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?
Options: a ) 22 hours , b ) 30 hours , c ) 44 hours , d ) 60 hours , e ) it can not be determined from the information above .
Rationale: "say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the t job in 44 hours . answer : c ."
Answer: c
Question (physics): a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 320 m long platform ?
Options: a ) 44 min , b ) 55 min , c ) 47 min , d ) 67 min , e ) 45 min
Rationale: "a 44 min let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 320 ) / 36 * 5 / 18 = 44 min ."
Answer: a
Question (gain): the price of a book is increased from $ 300 to $ 450 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "explanation : change in the price = rs 450 â € “ rs 300 = rs 150 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 150 300 ) * 100 = 50 % d"
Answer: d
Question (physics): a man can row downstream at 26 kmph and upstream at 22 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 24 , 2 , b ) 12 , 6 , c ) 15 , 3 , d ) 14 , 4 , e ) none of these
Rationale: "explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 26 - - - ( 1 ) and x - y = 22 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 48 = > x = 24 , y = 2 . answer : option a"
Answer: a
Question (physics): a train is walking at 6 / 7 of its usual speed , the train is 20 minutes too late . find its usual time to cover the journey .
Options: a ) 1 hour , b ) 30 min , c ) 3 hours 20 min , d ) 2 hours 30 min , e ) 2 hours
Rationale: new speed = 6 / 7 of the usual speed new time taken = 7 / 6 of the usual time taken so , ( 7 / 6 of the usual time ) - ( usual time ) = 20 min 1 / 6 of the usual time = 20 min usual time = 20 * 6 = 120 min = 2 hours correct option is e
Answer: e
Question (general): what is the sum of all remainders obtained when the first 110 natural numbers are divided by 9 ?
Options: a ) 397 , b ) 401 , c ) 403 , d ) 405 , e ) 399
Rationale: "a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such blocks , since 99 / 9 = 11 . the last will be : 91 divided by 9 gives the remainder of 1 ; 92 divided by 9 gives the remainder of 2 ; . . . 98 divided by 9 gives the remainder of 8 ; 99 divided by 9 gives the remainder of 0 . the last number , 100 , gives the remainder of 1 when divided by 9 , thus the sum of all remainders will be : 11 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0 ) + 1 = 403 . answer : c ."
Answer: c
Question (general): by how much is 30 % of 80 greater than 4 / 5 th of 25 ?
Options: a ) 2 , b ) 4 , c ) 10 , d ) 15 , e ) 17
Rationale: "answer it is ( 30 x 80 ) / 100 - ( 4 x 25 ) / 5 = 24 - 20 = 4 correct option : b"
Answer: b
Question (general): there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 77 . how tall is the fourth person ?
Options: a ) 79 , b ) 81 , c ) 83 , d ) 85 , e ) 87
Rationale: "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 77 ) = 308 x = 73 and the fourth person has a height of 73 + 10 = 83 inches the answer is c ."
Answer: c
Question (general): t = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set t and one integer from set b . what is the probability that the sum of the two integers will equal 9 ?
Options: a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33
Rationale: the total number of pairs t , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b .
Answer: b
Question (general): a man whose speed is 7 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 6.7 , b ) 4 , c ) 6 , d ) 9 , e ) 3
Rationale: "m = 7.0 s = 1.5 ds = 8.5 us = 5.5 as = ( 2 * 8.5 * 5.5 ) / 14 = 6.7 answer : a"
Answer: a
Question (gain): a sum was put at simple interest at a certain rate for 3 years . had it been put at 2 % higher rate , it would have fetched rs . 360 more . find the sum .
Options: a ) 3000 , b ) 6000 , c ) 2000 , d ) 4000 , e ) none of them
Rationale: "let sum = p and original rate = r . then , [ ( p * ( r + 2 ) * 3 ) / 100 ] – [ ( p * r * 3 ) / 100 ] = 360 . = 3 pr + 6 p - 3 pr = 36000  6 p = 36000  p = 6000 hence , sum = rs . 6000 . answer is b ."
Answer: b
Question (general): 30 ^ 10 / 210 ^ 5 = ?
Options: a ) 6 ^ 5 , b ) 5 ^ 6 , c ) ( 30 / 7 ) ^ 5 , d ) 6 ^ 3 , e ) 15 ^ 3
Rationale: "30 ^ 10 / 210 ^ 5 = ? a . 6 ^ 5 b . 5 ^ 6 c . ( 30 / 7 ) ^ 5 d . 6 ^ 3 e . 15 ^ 3 - > 30 ^ 10 / 210 ^ 5 = ( 30 ^ 10 ) / ( 7 ^ 5 ) ( 30 ^ 5 ) = ( 30 ^ 5 ) / ( 7 ^ 5 ) = ( 30 / 7 ) ^ 5 . thus , c is the answer ."
Answer: c
Question (general): the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 420 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .
Options: a ) 400 , b ) 420 , c ) 430 , d ) 450 , e ) 510
Rationale: "let no . of non - officers be x 15 * 420 + x * 110 = ( x + 15 ) 120 x = 450 d"
Answer: d
Question (general): if ( a - b - c + d = 13 ) and ( a + b - c - d = 9 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 . , e ) 64 .
Rationale: "eq 1 : a - b - c + d = 13 eq 2 : a + b - c - d = 9 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 13 - a + b - c - d = 9 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 4 ( 2 ) simplify - b + d = 2 b - d = - 2 ( b - d ) ^ 2 = ( - 2 ) ^ 2 = 4 my answer : a"
Answer: a
Question (other): in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 70 percent of the republicans and 25 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
Options: a ) 2 % , b ) 4 % , c ) 8 % , d ) 10 % , e ) 15 %
Rationale: 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 60 : 40 represents the number ratio of republicans : democrats . if 70 % of republicans ( which is ( 60 * 0.7 ) = 42 ) and 25 % of democrats ( 40 * 0.25 = 10 ) voted for candidate x , means that out of total of 100 voters ; 52 ( 42 + 10 ) voters voted for candidate x and 48 voted for candidate y . thus we can infer that candidate x is expected to win the election by 4 ( 52 - 48 ) votes . therefore candidate x is expected to win the election by ( 4 / 100 ) votes which is equivalent to 4 % . i think the answer is b .
Answer: b
Question (general): a family pays $ 800 per year for an insurance plan that pays 85 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total .
Options: a ) $ 1,100 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200
Rationale: "upfront payment for insurance plan = 800 $ family needs to pay 15 % of first 1000 $ in expense = 150 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 150 = 950 $ total amount paid by insurance plan for first 1000 $ = 800 $ total amount paid by family will equal amount paid by plan when medical expense = 1100 $ ( since insurance plan will pay 100 % of amount that exceeds 950 $ ) answer a"
Answer: a
Question (gain): a vendor bought toffees at 6 for a dollar . how many for a dollar must he sell to gain 20 % ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 9 , e ) 8
Rationale: "c 5 c . p . of 6 toffees = $ 1 s . p . of 6 toffees = 120 % of $ 1 = $ 6 / 5 for $ 6 / 5 , toffees sold = 6 . for $ 1 . toffees sold = 6 * 5 / 6 = 5"
Answer: c
Question (gain): if each year the population of the country grows by 100 % , how many years will elapse before the population of the country doubles ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "till year 2010 , population is 100 . year 2001 : population becomes 200 . . . . . . . . . . . . . 1 year elapsed answer : a"
Answer: a
Question (general): positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 50 . what is the value of x ?
Options: a ) 50 , b ) 100 , c ) 200 , d ) 140 , e ) 2,000
Rationale: "y = 50 % of 50 % 0 f x = x / 4 and y / 100 of x = 50 y / 100 * 4 y = 50 y = 35 and x = 140 answer - d"
Answer: d
Question (geometry): the number 149 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 19 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "2 ^ 2 + 8 ^ 2 + 9 ^ 2 = 149 - - > 2 + 9 + 8 = 19 . a"
Answer: a
Question (physics): a cube of side 8 meter length is cut into small cubes of side 16 cm each . how many such small cubes can be obtained ?
Options: a ) 10780 , b ) 127600 , c ) 125000 , d ) 152000 , e ) 10000
Rationale: "along one edge , the number of small cubes that can be cut = 800 / 16 = 50 along each edge 50 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 50 * 50 * 50 = 125000 answer : c"
Answer: c
Question (other): in a group of 28 junior high school students , 7 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 8 , d ) 4 , e ) 3
Rationale: "a 7 seven students are not taking a language . add 7 + 10 + 4 to get 21 . then subtract 21 from the total students : 28 - 21 = 7 ."
Answer: a
Question (gain): on selling 17 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "( c . p . of 17 balls ) - ( s . p . of 17 balls ) = ( c . p . of 5 balls ) c . p . of 12 balls = s . p . of 17 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 12 = rs . 60 . answer : e"
Answer: e
Question (geometry): the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 384 square centimeters , what is the length of the rectangle in centimeters ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 384 2 l ^ 2 / 3 = 384 l ^ 2 = 576 l = 24 cm the answer is e ."
Answer: e
Question (general): a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 5.0 . if the company ’ s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,500 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 2,250
Rationale: "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 5 $ then total value is 300 * 5.0 = 1500 . imo option b is correct answer . ."
Answer: b
Question (gain): ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 12880 , b ) 12789 , c ) 27108 , d ) 17600 , e ) 18291
Rationale: "explanation : price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 16000 * 110 / 100 = rs . 17600"
Answer: d
Question (general): 9873 + x = 13200 , then x is ?
Options: a ) 3327 , b ) 3237 , c ) 3337 , d ) 2337 , e ) none of these
Rationale: "answer x = 13200 - 9873 = 3327 option : a"
Answer: a
Question (general): a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 5 days starting with sunday is
Options: a ) 1215 , b ) 1314 , c ) 2900 , d ) 1710 , e ) 2750
Rationale: "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 × 5 + 240 × 25 / 30 ) = ( 8550 / 5 ) = 1710 answer : option d"
Answer: d
Question (gain): in an election , candidate a got 70 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ?
Options: a ) 355600 , b ) 355800 , c ) 356500 , d ) 356800 , e ) 333200
Rationale: total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 70 % therefore , the number of valid votes polled in favour of candidate a = 70 % of 476000 = 70 / 100 × 476000 = 33320000 / 100 = 333200 e )
Answer: e
Question (general): a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 5 , which can be repeated . if the product of the digits in the area code must be odd , how many different codes can be created ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 1 , e ) 30
Rationale: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 555 will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = ( total ) - ( restriction ) = 27 - 26 = 1 . answer : d ."
Answer: d
Question (general): if a * b denotes the greatest common divisor of a and b , then ( ( 12 * 16 ) * ( 30 * 24 ) ) = ?
Options: a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2
Rationale: "the greatest common divisor of 12 and 16 is 4 . hence 12 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 30 and 24 is 6 . hence 30 * 24 = 6 . hence ( ( 12 * 16 ) * ( 30 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ."
Answer: e
Question (general): a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 60 , how many horses are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "legs 12 * 4 = 48 now half on their horses so remaining on the walk so 6 men 6 men has 12 legs so , 12 + 48 = 60 legs walking answer : b"
Answer: b
Question (gain): in a certain parking lot , 2 % of the cars are towed for parking illegally . however 90 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ?
Options: a ) 10 % , b ) 12 % , c ) 16 % , d ) 18 % , e ) 20 %
Rationale: "let x be the number of cars and let y be the number of cars parked illegally . 2 % * x = 10 % * y y / x = 1 / 5 = 20 % the answer is e ."
Answer: e
Question (gain): a certain sky blue paint contains 10 percent blue pigment and 90 percent red pigment by weight . a certain green paint contains 70 percent blue pigment and 30 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5
Rationale: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 9 = 4.5 grams of red pigment
Answer: d
Question (general): alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 985 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20
Rationale: explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 985 96 + 225 + 490 + 6 x = 985 6 x = 174 = > x = 29 . answer : c
Answer: c
Question (physics): excluding stoppages , the speed of a bus is 65 kmph and including stoppages , it is 48 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 70 min , b ) 15 min , c ) 20.4 min , d ) 15.6 min , e ) 40 min
Rationale: "d 15.6 min due to stoppages , it covers 17 km less . time taken to cover 17 km = ( 17 / 65 x 60 ) min = 15.6 min"
Answer: d
Question (gain): a and b ’ s salaries together amount to rs . 2,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is b ’ s salary ?
Options: a ) 777 , b ) 500 , c ) 789 , d ) 776 , e ) 881
Rationale: "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 2000 4 b = 2000 = > b = 500 answer b"
Answer: b
Question (physics): the inner circumference of a circular race track , 14 m wide is 440 m . find the radius of the outer circle .
Options: a ) 84 , b ) 12 , c ) 67 , d ) 28 , e ) 21
Rationale: "explanation : let inner radius be r meters . { \ color { black } then , 2 \ pi r = 440 \ rightarrow r = 440 \ times \ frac { 7 } { 22 } \ times \ frac { 1 } { 2 } = 70 m } radius of outer circle = 70 + 14 = 84 m answer : a ) 84 m"
Answer: a
Question (geometry): the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 42
Rationale: "explanation : a / 8 = 8 * 8 = > a = 8 * 8 * 8 x * 2 x = 8 * 8 * 8 x = 16 = > 2 x = 32 answer : option b"
Answer: b