Cheukting/mathqa huggingface dataset:
Question (physics): a train of 30 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?
Options: a ) 6 , b ) 3.3 , c ) 4 , d ) 9 , e ) 2
Rationale: "d = 30 * 60 + 1500 = 3300 m t = 3300 / 60 * 18 / 5 = 198 sec = 3.3 mins answer : b"
Answer: b
Question (gain): in the manufacture of a certain product , 8 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 ?
Options: a ) 0.2 % , b ) 0.4 % , c ) 0.8 % , d ) 1.2 % , e ) 2.0 %
Rationale: "0.08 * 0.05 = 0.004 = 0.4 % the answer is b ."
Answer: b
Question (general): a number when divided by 779 gives a remainder 47 . by dividing the same number by 19 , what would be the remainder ?
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: "number = ( 779 x a ) + 47 , where ` ` a ' ' is the quotient = ( 19 x 41 x a ) + ( 19 x 2 ) + 9 = 19 x ( 41 a + 2 ) + 9 = 19 x ( new quotient ) + 9 \ inline \ fn _ jvn \ therefore required remainder = 9 answer : a"
Answer: a
Question (gain): a and b start a business , with a investing the total capital of rs . 10000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 1000 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ?
Options: a ) a ) 59000 , b ) b ) 37000 , c ) c ) 48000 , d ) d ) 59000 , e ) e ) 67000
Rationale: "interest received by a from b = 10 % of half of rs . 10000 = 10 % * 5000 = 500 . amount received by a per annum for being a working partner = 1000 * 12 = rs . 12000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 500 + 12000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 500 + 12000 + p ) = 2 ( p ) p = 12500 total profit = 2 p + 12000 = 2 * 12500 + 12000 = 37000 answer : b"
Answer: b
Question (physics): a train covers a distance of 100 km in 1 hour . if its speed is decreased by 15 km / hr , the time taken by the car to cover the same distance will be ?
Options: a ) 1 hr , b ) 1 hr 10 min , c ) 50 min , d ) 1 hr 30 min , e ) 1 hr 45 min
Rationale: "speed = 100 / 1 = 100 km / hr new speed = 100 - 15 = 85 km / hr time taken = 100 / 85 = 1 hr 10 min answer is b"
Answer: b
Question (general): if z is a multiple of 8778 , what is the remainder when z ^ 2 is divided by 9 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "the sum of the digits is 8 + 7 + 7 + 8 = 30 . thus 3 is a factor of 8778 , so 3 is a factor of z . then 3 ^ 3 = 9 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 9 is 0 . the answer is a ."
Answer: a
Question (physics): what is the least number of squares tiles required to pave the floor of a room 4 m 5 cm long and 2 m 25 cm broad ?
Options: a ) 14 , b ) 20 , c ) 40 , d ) 44 , e ) 45
Rationale: "length of largest tile = h . c . f . of 405 cm and 225 cm = 45 cm . area of each tile = ( 45 x 45 ) cm 2 . required number of tiles = 405 x 225 / ( 45 ^ 2 ) = 45 . answer : e"
Answer: e
Question (gain): $ 4,000 is deposited in a savings account that pays 8 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?
Options: a ) $ 4326.40 , b ) $ 4116.20 , c ) $ 4256.21 , d ) $ 4316.54 , e ) $ 4312.45
Rationale: "this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 8 / 2 = 4 % now , ca = 4000 ( 1 + 4 / 100 ) ^ 2 = $ 4326.40 hence answer is a"
Answer: a
Question (gain): the cost price of 30 articles is the same as the selling price of x articles . if the profit is 20 % , what is x ?
Options: a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "let the cost price = y the cost price of 30 articles = 30 y the selling price of x articles = 1.20 y * x 1.20 y * x = 30 y x = 30 / 1.2 = 25 the answer is d ."
Answer: d
Question (other): if 32.5 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 110 , b ) 330 , c ) 550 , d ) 594 , e ) 880
Rationale: "students enrolled in biology are 32.5 % and therefore not enrolled are 67.5 % . so of 880 is 880 * . 675 = 594 answer is d 594"
Answer: d
Question (physics): a train which has 430 m long , is running 45 kmph . in what time will it cross a person moving at 9 kmph in same direction ?
Options: a ) 56 sec , b ) 43 sec , c ) 36 sec , d ) 29 sec . , e ) 19 sec .
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 430 / ( ( 45 - 9 ) ( 5 / 18 ) = 430 / 36 * ( 5 / 18 ) = 430 / 10 = 43 sec answer : b"
Answer: b
Question (gain): a sum fetched a total simple interest of $ 4151.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8928
Rationale: "e 8928 principal = $ 100 x 4151.25 / 9 x 5 = $ 415125 / 45 = $ 8928 ."
Answer: e
Question (physics): a certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 6 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: "total time for travelling 80 miles @ 60 mph = 80 / 60 = 4 / 3 hour = 80 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 60 mph . thus in 80 minutes it will use = 2 gallons . thus , full tank = 2 + 6 = 8 gallons - - - > 2 / 8 = 25 % of the fuel used . c is the correct answer ."
Answer: c
Question (physics): a car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for the rest of the trip . if the average speed for the entire trip is 34 miles per hour , how many hours long is the trip ?
Options: a ) 6.5 , b ) 7.5 , c ) 8.5 , d ) 9.5 , e ) 10.5
Rationale: let t be the total time of the trip . 30 * 5 + 42 ( t - 5 ) = 34 t 8 t = 210 - 150 t = 7.5 the answer is b .
Answer: b
Question (gain): what will be the compound interest on a sum of rs . 29,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 11123.77 , b ) s . 11742.91 , c ) s . 11123.20 , d ) s . 10123.28 , e ) s . 10123.21
Rationale: "amount = [ 29000 * ( 1 + 12 / 100 ) 3 ] = 29000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 40742.91 c . i . = ( 40742.91 - 29000 ) = rs . 11742.91 answer : b"
Answer: b
Question (physics): if jack walked 6 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ?
Options: a ) 4 , b ) 4.8 , c ) 6 , d ) 6.25 , e ) 15
Rationale: "distance walked in 1 hour and 15 mins = 6 miles speed per hour = distance / time = 6 / ( 5 / 4 ) = 4.8 miles per hour answer b"
Answer: b
Question (general): in a group of cows and hens , the number of legs are 8 more than twice the number of heads . the number of cows is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 10 , e ) 4
Rationale: let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 8 2 x = 8 x = 4 . answer : e
Answer: e
Question (general): the number of positive integer solutions for the equation x + y + z + t = 30 is
Options: a ) 3854 , b ) 3654 , c ) 3764 , d ) 3960 , e ) 4964
Rationale: "the number of positive integer solutions for the equatio fx 1 + x 2 + ⋯ + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 30 - 1 c 4 - 1 = 29 c 3 = 3654 answer : b"
Answer: b
Question (general): reeya obtained 55 , 67 , 76 , 82 and 85 out of 100 in different subjects , what will be the average
Options: a ) 70 , b ) 75 , c ) 73 , d ) 85 , e ) 90
Rationale: "explanation : ( 55 + 67 + 76 + 82 + 85 / 5 ) = 73 option c"
Answer: c
Question (other): there are two positive numbers in the ratio 2 : 7 . if the larger number exceeds the smaller by 30 , then find the larger number ?
Options: a ) 42 , b ) 38 , c ) 44 , d ) 36 , e ) 46
Rationale: "let the two positive numbers be 2 x and 7 x respectively . 7 x - 2 x = 30 5 x = 30 = > x = 6 = > larger number = 7 x = 42 . answer : a"
Answer: a
Question (gain): one night 17 percent of the female officers on a police force were on duty . if 204 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 420 , b ) 480 , c ) 540 , d ) 600 , e ) 660
Rationale: "let x be the number of female police officers on the police force . the number of female police officers on duty was 102 . 0.17 x = 102 x = 600 the answer is d ."
Answer: d
Question (general): the contents of a certain box consist of 20 apples and 30 oranges . how many oranges must be added to the box so that exactly 20 % of the pieces of fruit in the box will be apples ?
Options: a ) 50 , b ) 55 , c ) 75 , d ) 85 , e ) 100
Rationale: "apple = ( apple + orange + x ) * 0.2 20 = ( 30 + 20 + x ) * 0.2 x = 50 answer : a"
Answer: a
Question (gain): the workforce of company x is 60 % female . the company hired 24 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 288 , d ) 360 , e ) 420
Rationale: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 24 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 24 ) 0.05 x = 13.2 x = 264 - this is quantity of employees before adding 24 men so after adding it will be 288 answer is c"
Answer: c
Question (general): whats the reminder when 58 , 458,965 , 231,457 , 895,684 , 525,465 , 985,445 is divided by 16
Options: a ) 5 , b ) 7 . , c ) 2 . , d ) 3 , e ) 9
Rationale: "a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . a number ending in 3 zeroes is divisible by 8 . a number ending in 4 zeroes in divisible by 16 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 58 , 458,965 , 231,457 , 895,684 , 525,465 , 985,445 = 58 , 458,965 , 231,457 , 895,684 , 525,465 , 980,000 + 5,445 the first number is divisible by 16 . you just have to find the remainder when you divide 5445 by 16 . that will be the remainder when you divide the original number by 16 . 5445 / 16 gives remainder 5 . answer ( a )"
Answer: a
Question (geometry): the ratio of the volumes of two cubes is 1000 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 100 : 121 , b ) 100 : 127 , c ) 81 : 191 , d ) 81 : 161 , e ) 100 : 182
Rationale: "explanation : ratio of the sides = ³ √ 1000 : ³ √ 1331 = 10 : 11 ratio of surface areas = 10 ^ 2 : 11 ^ 2 = 100 : 121 answer : option a"
Answer: a
Question (general): what is the smallest positive integer x such that 720 - x is the cube of a positive integer
Options: a ) 5 , b ) 7 , c ) 47 , d ) 9 , e ) 12
Rationale: "given 738 - x is a perfect cube so we will take 729 = 9 * 9 * 9 738 - x = 729 x = 738 - 729 = 9 correct option is d"
Answer: d
Question (general): 1370 , x , 1070 , - 180 , - 6430
Options: a ) 1320 , b ) 6530 , c ) 6630 , d ) 6730 , e ) 6830
Rationale: 1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a .
Answer: a
Question (other): if 75 percent of a class answered the first question on a certain test correctly , 45 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 10 % , b ) ( 8 ) 40 % , c ) 30 % , d ) 50 % , e ) 65 %
Rationale: "i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 75 - x ) + x + ( 45 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 120 x = 40 ans : b"
Answer: b
Question (geometry): the perimeter of a square is equal to the perimeter of a rectangle of length 17 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 23.57 , b ) 23.54 , c ) 23.5 , d ) 24.35 , e ) 24.51
Rationale: "let the side of the square be a cm . perimeter of the rectangle = 2 ( 17 + 14 ) = 62 cm perimeter of the square = 62 cm i . e . 4 a = 62 a = 15.5 diameter of the semicircle = 15.5 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 15.5 ) = 1 / 2 ( 22 / 7 ) ( 15.5 ) = 24.35 cm to two decimal places answer : d"
Answer: d
Question (gain): ? % of 360 = 180
Options: a ) 277 , b ) 36 , c ) 50 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 180 or , ? = 180 × 100 / 360 = 50 answer c"
Answer: c
Question (general): the average of runs of a cricket player of 10 innings was 33 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 77 , b ) 79 , c ) 85 , d ) 87 , e ) 89
Rationale: "explanation : average = total runs / no . of innings = 33 so , total = average x no . of innings = 33 x 10 = 330 . now increase in avg = 4 runs . so , new avg = 33 + 4 = 37 runs total runs = new avg x new no . of innings = 37 x 11 = 407 runs made in the 11 th inning = 407 - 330 = 77 answer : a"
Answer: a
Question (general): if y exceeds x by 25 % , then x is less than y by ?
Options: a ) 28 % , b ) 21 % , c ) 20 % , d ) 30 % , e ) 29 %
Rationale: "x = 100 y = 125 125 - - - - - - - - 25 100 - - - - - - - - ? = > 20 % answer : c"
Answer: c
Question (general): the average score of a cricketer in 2 matches is 60 and in other 3 matches is 50 . then find the average score in all the 5 matches ?
Options: a ) 54 , b ) 27 , c ) 30 , d ) 35 , e ) 42
Rationale: "average in 5 matches = ( 2 * 60 + 3 * 50 ) / 2 + 3 = 120 + 150 / 5 = 270 / 5 = 54 answer is a"
Answer: a
Question (geometry): the largest three digit number which is a perfect cube , is :
Options: a ) 125 , b ) 999 , c ) 343 , d ) 512 , e ) 729
Rationale: "explanation : 9 * 9 * 9 = 729 answer : e"
Answer: e
Question (physics): a 160 meter long train crosses a man standing on the platform in 18 sec . what is the speed of the train ?
Options: a ) 96 kmph , b ) 94 kmph , c ) 32 kmph , d ) 56 kmph , e ) 76 kmph
Rationale: "s = 160 / 18 * 18 / 5 = 32 kmph answer : c"
Answer: c
Question (gain): albert invested rs . 8000 in a scheme for 2 years at compound interest rate 5 % p . a . how much amount will albert get on maturity of the fixed deposit ?
Options: a ) 8840 , b ) 2776 , c ) 2998 , d ) 2662 , e ) 8820
Rationale: "amount = [ 8000 * ( 1 + 5 / 100 ) 2 ] = 8000 * 21 / 20 * 21 / 20 = rs . 8820 answer : e"
Answer: e
Question (gain): a person buys an article at $ 600 . at what price should he sell the article so as to make a profit of 8 % ?
Options: a ) 670 , b ) 689 , c ) 648 , d ) 740 , e ) 889
Rationale: "c 648 cost price = $ 600 profit = 8 % of 600 = $ 48 selling price = cost price + profit = 600 + 48 = 648"
Answer: c
Question (general): what is the remainder when ( 63 ) ( 65 ) is divided by 8 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7
Rationale: "( 63 ) ( 65 ) = ( 64 - 1 ) ( 64 + 1 ) = 64 ^ 2 - 1 which is 1 less than a multiple of 8 . then the remainder will be 7 . the answer is e ."
Answer: e
Question (other): if shares of two persons in profits are rs . 1600 and rs . 1200 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: "profit = time * capital so 1600 : 1200 = 4 : 3 answer : c"
Answer: c
Question (other): irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 148 cookies , what percent of the cookies did ingrid bake ?
Options: a ) 0.125 % , b ) 1.25 % , c ) 31.7 % , d ) 125 % , e ) 0.152 %
Rationale: 9.18 x + 5.17 x + 2.05 x = 16.4 x = 148 cookies x = 148 / 16.4 = 9 ( approx ) so , ingrid baked 9 * 5.17 cookies or 47 cookies ( approx ) % share = 47 / 148 = 31.7 approx hence , answer is c .
Answer: c
Question (other): two integers are in the ratio of 1 to 4 . if 6 is added to the smaller number , the ratio becomes 1 to 3 . find the larger integer .
Options: a ) 4 , b ) 24 , c ) 30 , d ) 72 , e ) 80
Rationale: "one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 4 , then 4 x = y , where x is the smaller integer . if adding 6 to the smaller integer makes the ratio 1 to 3 , then 3 ( x + 6 ) = y . substituting y = 4 x into the second equation yields 3 x + 18 = 4 x . so , x = 18 ( smaller integer ) and , y = 4 x = 72 ( larger integer ) so d is the correct answer . another option is to test the answer choices . a ) the larger number is 4 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 1 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 1 ) , we get 7 . so , the new ratio is 7 to 4 . no good . we want a resulting ratio of 1 to 3 eliminate a b ) the larger number is 24 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 6 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 6 ) , we get 12 so , the new ratio is 12 to 24 which is 1 to 2 . no good . we want a resulting ratio of 1 to 3 eliminate b c ) the larger number is 30 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 7.5 ( which is not an integer ) since both numbers are integers , the larger number can not be 30 . eliminate c d ) the larger number is 72 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 18 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 18 ) , we get 24 so , the new ratio is 24 to 72 . this is the same as the ratio of 1 to 3 therefore ( d ) is correct e ) the larger number is 80 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 20 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 20 ) , we get 26 so , the new ratio is 26 to 80 which is 13 to 40 . no good . we want a resulting ratio of 1 to 3 eliminate e therefore d is the only correct choice ."
Answer: d
Question (general): a , b and c are partners in a business . their capitals are respectively , rs . 5000 , rs . 6000 and rs . 4000 . a gets 30 % of the total profit for managing the business . the remaining profit is divided among 3 in the ratio of their capitals . in the end of the year , the profit of a is rs . 200 more than the sum of the profits of b and c . find the total profit ?
Options: a ) 3089 , b ) 3098 , c ) 3057 , d ) 3000 , e ) 3012
Rationale: a : b : c = 5 : 6 : 4 let the total profit = 100 - 30 = 70 5 / 15 * 70 = 70 / 3 a share = 70 / 3 + 30 = 160 / 3 b + c share = 100 - 160 / 3 = 140 / 3 a - ( b + c ) = 160 / 3 - 140 / 3 = 20 / 3 20 / 3 - - - - 200 100 - - - - ? = > 3000 answer : d
Answer: d
Question (general): $ 100 is divided amongst a , b and c so that a may get 1 / 4 as much as b and c together , b may get 3 / 5 as much as a and c together , then the share of a is
Options: a ) $ 15 , b ) $ 20 , c ) $ 25 , d ) $ 18 , e ) $ 30
Rationale: "a : ( b + c ) = 1 : 4 a ' s share = 100 * 1 / 5 = $ 20 answer is b"
Answer: b
Question (probability): an urn contains 5 red , 6 blue and 8 green balls . 4 balls are randomly selected from the urn , find the probability that the drawn ball are 1 blue and 3 red ?
Options: a ) 1 / 969 , b ) 2 / 969 , c ) 4 / 969 , d ) 5 / 323 , e ) 21 / 789
Rationale: sample space = no . of ways 4 balls were drawn from urn = 19 c 4 = 3876 no . ways 1 blue balls and 3 red were drawn from bag = 6 c 1 * 5 c 3 = 60 probability = 60 / 3876 = 5 / 323 ans - d
Answer: d
Question (general): how many positive even integers less than 100 contain digits 5 or 9 ?
Options: a ) 16 , b ) 10 , c ) 18 , d ) 19 , e ) 20
Rationale: two digit numbers : 5 at tens place : 50 , 52,54 , 56,58 9 at tens place : 90 , 92,94 , 96,98 if 5 and 9 is at units place , the number cant be even total : 5 + 5 = 10 answer b
Answer: b
Question (general): farm tax is levied on the 45 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 15.125 % , d ) 27.78 % , e ) none
Rationale: "only trick n this question is to ignore 45 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 45 ) = 27.78 % and the answer is not there in the options . the correct answer is ( d ) ."
Answer: d
Question (general): 30 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :
Options: a ) 33 , b ) 34 , c ) 26 , d ) 10 , e ) 19
Rationale: "explanation : let the two parts be ( 30 - x ) and x . then , 10 ( 30 - x ) + 22 x = 780 = > 12 x = 480 = > x = 40 . bigger part = ( 30 - x ) = 10 . answer : d ) 10"
Answer: d
Question (gain): the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 30,000 is made ?
Options: a ) 328897 , b ) 120000 , c ) 877888 , d ) 277768 , e ) 126000
Rationale: "the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 30,000 is made = 96,000 + 30,000 = rs . 1 , 26,000 answer : e"
Answer: e
Question (physics): johnson completes a piece of work in 10 days , vincent completes the same work in 40 days . if both of them work together , then the number of days required to complete the work is
Options: a ) 7 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 12 days
Rationale: if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 10 × 40 / 50 = 8 days . b )
Answer: b
Question (geometry): in triangle pqr , the angle q = 90 degree , pq = 4 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 ) 1.2 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 : 4 = 8 : 10 - - > qy = 3.2 . answer : e"
Answer: e