Cheukting/mathqa huggingface dataset:
Question (general): a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , then how old is b ?
Options: a ) 17 years , b ) 19 years , c ) 29 years , d ) 10 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 = > x = 6 hence , b ' s age = 2 x = 12 years . answer : e"
Answer: e
Question (general): evaluate : 6702.5 + 670.25 + 67.025 + 6.7025 + 0.67025
Options: a ) 7447.14775 , b ) 6981.59775 , c ) 6918.59775 , d ) 6198.59775 , e ) 6891.59775
Rationale: "6702.5 670.25 67.025 6.7025 + 0.67025 - - - - - - - - - - - - - - - 7447.14775 answer is a ."
Answer: a
Question (geometry): a cylindrical can has a radius of 4 centimeters and a height of 24 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ?
Options: a ) 16 pi , b ) 64 pi , c ) 96 pi , d ) 192 pi , e ) 576 pi
Rationale: "they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 4 * 24 = 192 pi answer is d ."
Answer: d
Question (physics): it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 12 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
Options: a ) 10 min . , b ) 41 min . , c ) 17 min . , d ) 23 min . , e ) 20 min .
Rationale: the ratio is 2 : 3 = gym : ride , so ( 12 ) ( 3 / 2 ) = 18 minutes at the gym , and 18 + 12 = 30 minutes exercise , so ( 2 / 3 ) ( 30 ) = 20 minutes yoga . answer : e
Answer: e
Question (general): the probability that a man will be alive for 10 more yrs is 3 / 4 & the probability that his wife will alive for 10 more yrs is 3 / 7 . the probability that none of them will be alive for 10 more yrs , is
Options: a ) 1 / 2 , b ) 1 , c ) 1 / 7 , d ) 3 / 4 , e ) 2
Rationale: "sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 7 ans . ( c )"
Answer: c
Question (general): a jar of 264 marbles is divided equally among a group of marble - players . if 2 people join the group , each one would receive 1 marble less . how many people are there in the group today ?
Options: a ) 20 , b ) 21 . , c ) 22 , d ) 23 , e ) 24
Rationale: "only 22 and 24 divide 264 perfectly , assume initially , there are 22 people , , each will get 12 marbles two people join , then 24 will get 11 marble each . hence answer e = 24"
Answer: e
Question (other): two numbers are in the ratio 3 : 4 . if the sum of numbers is 63 , find the numbers .
Options: a ) 27 and 36 . , b ) 25 and 30 . , c ) 23 and 44 . , d ) 63 and 12 . , e ) 12 and 36 .
Rationale: "sum of the terms of the ratio = 3 + 4 = 7 sum of numbers = 63 therefore , first number = 3 / 7 × 63 = 27 second number = 4 / 7 × 63 = 36 therefore , the two numbers are 27 and 36 . answer is a"
Answer: a
Question (general): a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food , and 1 / 8 of his salary on conveyance . if he has rs 1400 left with him , find his expenditure on food and conveyance
Options: a ) 3200 , b ) 3400 , c ) 3600 , d ) 3800 , e ) 4000
Rationale: "if his salary is x , then x - x * ( 2 / 5 + 3 / 10 + 1 / 8 ) = 1400 x ( 1 - 33 / 40 ) = 1400 x = 1400 * 40 / 7 = rs 8000 expenditure on food and conveyance = 8000 * 3 / 10 + 8000 * 1 / 8 = 2400 + 1000 = 3400 answer : b"
Answer: b
Question (general): a certain bus driver is paid a regular rate of $ 14 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 54 , b ) 51 , c ) 59 , d ) 55 , e ) 52
Rationale: "for 40 hrs = 40 * 14 = 560 excess = 976 - 560 = 416 for extra hours = . 75 ( 14 ) = 10.5 + 14 = 24.5 number of extra hrs = 416 / 24.5 = 18.82 = 19 approx . total hrs = 40 + 19 = 59 answer c 59"
Answer: c
Question (physics): a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 3 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 360 , b ) 487 , c ) 481 , d ) 729 , e ) 268
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 3 = 360 answer : a"
Answer: a
Question (other): the ratio of the incomes of a and b is 2 : 3 and the ratio of their expenditure is 1 : 2 . if at the end of the year , each saves $ 500 then the income of a is ?
Options: a ) $ 1000 , b ) $ 1500 , c ) $ 1200 , d ) $ 900 , e ) $ 1100
Rationale: "let the income of a and b be $ 2 x and $ 3 x let their expenditures be $ y and $ 2 y 2 x - y = 500 - - - - - - - 1 ) 3 x - 2 y = 500 - - - - - - - 2 ) from 1 ) and 2 ) x = 500 a ' s income = 2 x = 2 * 500 = $ 1000 answer is a"
Answer: a
Question (gain): the compound and the simple interests on a certain sum at the same rate of interest for two years are rs . 11730 and rs . 10200 respectively . find the sum
Options: a ) rs . 17037 , b ) rs . 17000 , c ) rs . 17276 , d ) rs . 170287 , e ) rs . 171881
Rationale: explanation : the simple interest for the first year is 10200 / 2 is rs . 5100 and compound interest for first year also is rs . 5100 . the compound interest for second year on rs . 5100 for one year so rate of the interest = ( 100 * 1530 ) / ( 5100 * 1 ) = 30 % p . a . so p = ( 100 * 10200 ) / ( 30 * 2 ) = rs . 17000 answer : b
Answer: b
Question (general): the sum of two numbers is 8 and the sum of their squares is 120 . find the product of the two numbers .
Options: a ) 25 , b ) 24 , c ) 23 , d ) 21 , e ) 28
Rationale: let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 8 a ^ 2 + b ^ 2 = 120 so , 8 ^ 2 = 120 + 2 ab 2 ab = 120 - 64 2 ab = 56 ab = 28 ans e
Answer: e
Question (gain): if the cost price of 121 chocolates is equal to the selling price of 77 chocolates , the gain percent is :
Options: a ) 56.14 % , b ) 57.44 % , c ) 57.14 % , d ) 56.34 % , e ) 57.87 %
Rationale: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 77 chocolates = rs . 77 ; s . p . of 77 chocolates = rs . 121 . . ' . gain % = 44 * 100 / 77 = 57.14 % answer : c"
Answer: c
Question (general): a library has an average of 500 visitors on sundays and 140 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 550
Rationale: "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 500 * 5 + 140 * 25 ) / 30 = 6000 / 30 = 200 answer : b ) 200"
Answer: b
Question (gain): a man can row his boat with the stream at 6 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 7
Rationale: "ds = 6 us = 4 s = ? s = ( 6 - 4 ) / 2 = 1 kmph answer : a"
Answer: a
Question (gain): a man buys 100 lts of liquid which contains 25 % of the liquid and the rest is water . he then mixes it with 90 lts of another mixture with 30 % of liquid . what is the % of water in the new mixture ?
Options: a ) 81 , b ) 75 , c ) 72.63 , d ) 73 , e ) 76
Rationale: 25 % in 100 lts is 25 . so water = 100 - 25 = 75 lts . 30 % of 90 lts = 27 . so water in 2 nd mixture = 90 - 27 = 63 lts . now total quantity = 100 + 90 = 190 lts . total water in it will be 75 + 63 = 138 lts . % of water = ( 100 * 138 ) / 190 = 72.63 answer : c
Answer: c
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 3 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 170 meter , c ) 156 meter , d ) 168 meter , e ) 50 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 3 = 50 meter answer : e"
Answer: e
Question (gain): the sale price sarees listed for rs . 750 after successive discount is 20 % and 15 % is ?
Options: a ) 227 , b ) 570 , c ) 342 , d ) 680 , e ) 230
Rationale: "750 * ( 80 / 100 ) * ( 85 / 100 ) = 570 answer : b"
Answer: b
Question (general): operation # is defined as adding a randomly selected two digit multiple of 10 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ?
Options: a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 %
Rationale: "any multiple of 10 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a ."
Answer: a
Question (physics): a room of 8 m 44 cm long and 3 m 50 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 73850 , b ) 73805 , c ) 844 , d ) 350 , e ) 2
Rationale: "explanation : area of the room = 844 * 350 sq cm size of largest square tile = h . c . f of 844 cm and 350 cm = 2 cm area of 1 tile = 2 * 2 sq cm no . of tiles required = ( 844 * 350 ) / ( 2 * 2 ) = 73850 answer : a ) 73850"
Answer: a
Question (physics): a train leaves mumabai at 9 am at a speed of 40 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 45 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 287 , b ) 279 , c ) 270 , d ) 278 , e ) 379
Rationale: "when the second train leaves mumbai the first train covers 40 * 1 = 40 km so , the distance between first train and second train is 40 km at 10.00 am time taken by the trains to meet = distance / relative speed = 40 / ( 45 - 40 ) = 8 hours so , the two trains meet at 6 p . m . the two trains meet 6 * 45 = 270 km away from mumbai . answer : c"
Answer: c
Question (general): he average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 62 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 55 kg , c ) 45 kg , d ) 85 kg , e ) 90 kg
Rationale: "explanation : total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 62 + 28 ) kg = 90 kg . answer : e"
Answer: e
Question (gain): the price of a jacket is reduced by 20 % . during a special sale the price of the jacket is reduced another 25 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 32.5 , b ) 35 , c ) 48.1 , d ) 65 , e ) 66.67
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 20 % , therefore bringing down the price to $ 80 . 3 ) again it is further discounted by 25 % , therefore bringing down the price to $ 60 . 4 ) now 60 has to be added byx % in order to equal the original price . 60 + ( x % ) 60 = 100 . solving this eq for x , we get x = 66.67 ans is e ."
Answer: e
Question (geometry): a cylindrical can has a radius of 3 centimeters and a height of 12 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ?
Options: a ) 16 pi , b ) 72 pi , c ) 96 pi , d ) 192 pi , e ) 576 pi
Rationale: "they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 3 * 12 = 72 pi answer is b ."
Answer: b
Question (gain): a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 9.00 ?
Options: a ) 40 , b ) 60 , c ) 90 , d ) 120 , e ) 108
Rationale: "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 9 ( 1 / 12 ) * x = 9 x = 108 answer : e"
Answer: e
Question (gain): a man took a loan from a bank at the rate of 11 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
Options: a ) rs . 16363.64 , b ) rs . 10 , 000.64 , c ) rs . 15 , 000,64 , d ) rs . 21 , 353.64 , e ) none
Rationale: "solution principal = rs . ( 100 x 5400 / 11 x 3 ) = rs . 16363.64 . answer a"
Answer: a
Question (general): the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 98 , what is the difference between the ages of patrick and monica ?
Options: a ) 32 , b ) 48 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 49 x = 98 x = 2 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 2 = 32 answer a"
Answer: a
Question (general): three 6 faced dice are thrown together . the probability that exactly two dice show the same number on them is - .
Options: a ) 5 / 12 , b ) 4 / 13 , c ) 5 / 17 , d ) 3 / 12 , e ) 8 / 9
Rationale: "using question number 11 and 12 , we get the probability as 1 - ( 1 / 36 + 5 / 9 ) = 5 / 12 answer a"
Answer: a
Question (geometry): six dots are evenly spaced on the circumference of a circle . how many combinations of three dots can we make from these 6 dots that do not form an equilateral triangle ?
Options: a ) 18
b ) 17
c ) 16
d ) 15
e ) 14
Rationale: the total number of ways we can choose three dots is 6 c 3 = 20 . we can form two equilateral triangles from these six dots . there are 20 - 2 = 18 combinations which do not form an equilateral triangle . the answer is a .
Answer: a
Question (physics): nd the area of trapezium whose parallel sides are 20 cm and 16 cm long , and the distance between them is 15 cm ?
Options: a ) 270 cm 2 , b ) 275 cm 2 , c ) 280 cm 2 , d ) 285 cm 2 , e ) 290 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 16 ) * ( 15 ) = 270 cm 2 answer : a"
Answer: a
Question (general): how many positive integer solutions does the equation 2 x + 1 y = 100 have ?
Options: a ) 44 , b ) 33 , c ) 50 , d ) 35 , e ) 14
Rationale: "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 2 * 1 ) = 50 answer : c"
Answer: c
Question (general): if all the 6 are replaced by 9 , then the algebraic sum of all the numbers from 1 to 100 ( both inclusive ) varies by how much ?
Options: a ) 330 , b ) 360 , c ) 380 , d ) 400 , e ) 420
Rationale: "unit place increased by 3 . so 6 , 16,26 , . . . . 96 . total 10 * 3 = 30 increased . ten ' s place increased by 30 . so 60,61 , . . . 69 . total 10 * 30 = 300 increased . so total varies = 300 + 30 = 330 . answer : a"
Answer: a
Question (physics): a train 130 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 60 kmph , e ) 73 kmph
Rationale: "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 130 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2340 < = > x = 73 speed of the train is 73 kmph . answer : option e"
Answer: e
Question (general): sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6700 ?
Options: a ) 4966 , b ) 6191 , c ) 2877 , d ) 2676 , e ) 1881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6700 x 6 ) - 34009 ] = rs . ( 40200 - 34009 ) = rs . 6191 answer : b"
Answer: b
Question (general): find the average of all prime numbers between 10 and 40
Options: a ) 15.6 , b ) 22.5 , c ) 18.6 , d ) 32.2 , e ) 26.9
Rationale: "prime numbers between 10 and 40 are 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 required average = ( 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 ) / 8 = 180 / 8 = 22.5 answer is b"
Answer: b
Question (general): if y is 80 % greater than x , than x is what % less than y ?
Options: a ) 20 , b ) 25 , c ) 33 1 / 3 , d ) 44 4 / 9 , e ) 80
Rationale: "let x = 100 so y = 180 we want percentage change . so , ( 100 - 180 ) / 180 = - 44.44 % = 44 4 / 9 % lesser than y . hence option ( d ) ."
Answer: d
Question (physics): how many miles is 150 km ?
Options: a ) 91.5 miles , b ) 92.75 miles , c ) 93.75 miles , d ) 94.5 miles , e ) 95.75 miles
Rationale: "93.75 miles 150 / 1.6 answer : c"
Answer: c
Question (general): every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 108 , how many more green disks than blue disks are in the bag ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 40
Rationale: "let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 108 - - > x = 6 . g - b = 8 x - 3 x = 5 x = 30 . the answer is c ."
Answer: c
Question (general): a room is 7 meters 20 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 10 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "let us calculate both the length and width of the room in centimeters . length = 7 meters and 20 centimeters = 720 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 720 and 432 = 144 thus , the number of square tiles required = ( 720 x 432 ) / ( 144 x 144 ) = 5 x 3 = 15 answer : b"
Answer: b
Question (general): a number is greater than 3 but less than 8 . also the number is greater than 6 but less than 10 . what is the number ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 8 , e ) 9
Rationale: b 7
Answer: b
Question (physics): efrida and frazer who live 13 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is two miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "it ' s a simple geometry problem . look at the diagram below : answer : e ."
Answer: e
Question (physics): a cistern is filled by a tap in 8 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ?
Options: a ) 133 , b ) 143 , c ) 153 , d ) 163 , e ) 173
Rationale: "filling rate - leak rate = net rate 1 / 8.5 - leak rate = 1 / 9 leak rate = 2 / 17 - 1 / 9 = 1 / 153 the answer is c ."
Answer: c
Question (physics): nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 54 meter head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 15 seconds , b ) 18 seconds , c ) 25 seconds , d ) 27 seconds , e ) 45 seconds
Rationale: "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 54 for cristina = c = 5 * t @ t = 27 , n = 135 c = 135 right answer ans : d"
Answer: d
Question (physics): susan can type 10 pages in 5 minutes . mary can type 5 pages in 10 minutes . working together , how many pages can they type in 30 minutes ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 65 , e ) 75
Rationale: susan can type 2 pages in 1 min mary can type 0.5 pages in 1 min so , both of them work together they type 2.5 pages in 1 min so , in 30 min they type ( 30 * 2.5 ) = 75 pages answer : e
Answer: e
Question (general): ( 178 % of 1265 ) ÷ 5.96 = ?
Options: a ) 125 , b ) 175 , c ) 225 , d ) 375 , e ) 524
Rationale: explanation : ? = ( 178 x 1265 / 100 ) ÷ 6 = 2250 / 600 = 375 answer : option d
Answer: d
Question (other): at the faculty of aerospace engineering , 312 students study random - processing methods , 234 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?
Options: a ) 430 , b ) 434 , c ) 438 , d ) 444 , e ) 446
Rationale: "312 + 234 - 112 ( since 112 is counted twice ) = 434 b is the answer"
Answer: b
Question (other): there are 399 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?
Options: a ) 152 , b ) 209 , c ) 57 , d ) 231 , e ) 181
Rationale: "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 399 = 231 answer : d"
Answer: d
Question (general): after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 6100 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) 2400
Rationale: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 6100 = 21600 exp in % = 100 - 10 = 90 % , 21600 = 90 % saving = 10 % = 21600 x 10 / 90 = rs . 2400 answer : e"
Answer: e
Question (physics): a train 825 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 90 seconds . the speed of the train is :
Options: a ) 33 , b ) 27 , c ) 27 , d ) 50 , e ) 81
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 45 = = > x = 50 km / hr . answer : d"
Answer: d
Question (general): in a hostel , the number of students decreased by 10 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 7.4 %
Rationale: "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.9 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.9 * 1.2 ) = > f ( new ) = 0.9259 f therefore the new cost of food must be 92.59 % of the old cost , or the cost of food must decrease by 7.4 % ( option e )"
Answer: e
Question (physics): the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 63 kmph , find the speed of the stream ?
Options: a ) 15 , b ) 19 , c ) 14 , d ) 21 , e ) 16
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 63 / 3 = 21 kmph . answer : d"
Answer: d
Question (general): if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 6600 ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 10
Rationale: "required difference = [ 3 ½ % of rs . 6600 ] – [ 3 1 / 3 % of rs . 6600 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 6600 = 1 / 6 % of rs . 6600 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 6600 ] = rs . 11 . answer is a ."
Answer: a