shulijia/MNLP_M3_mathqa · Datasets at Hugging Face

choices dict	answerKey listlengths 1 1	question stringlengths 8 751	rationale stringlengths 8 1.53k	dataset stringclasses 1 value
{ "label": [ "A", "B", "C", "D" ], "text": [ "6 , 8", "9 , 12", "12 , 16", "16 , 20" ] }	[ "A" ]	two numbers are such that the square of one is 224 less than 8 times the square of the other . if the numbers be in the ratio of 3 : 4 , the numbers are	solution let the numbers be 3 x and 4 x . then , ( 4 x ) 2 = 8 x ( 3 x ) 2 - 224 ‹ = › 16 x 2 = 72 x 2 - 224 ‹ = › 56 x 2 = 224 . ‹ = › x 2 = 4 . ‹ = › x = 2 . so , the numbers are 6 and 8 . answer a	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "750", "400", "800", "850" ] }	[ "B" ]	in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 160 vote ’ s majority . what is the total number of votes polled ?	"explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 160 ( 40 * 4 = 160 ) 100 % - - - - - > 400 ( 100 * 4 = 400 ) answer : option b"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1865113", "1775123", "1764613", "1675123" ] }	[ "C" ]	( 4300231 ) - ? = 2535618	"let 4300231 - x = 2535618 then x = 4300231 - 2535618 = 1764613 answer is c"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "34", "25", "48", "50" ] }	[ "A" ]	the average of 40 results is 30 and the average of other 30 results is 40 . what is the average of all the results ?	answer sum of 70 result = sum of 40 result + sum of 30 result . = 40 x 30 + 30 x 40 = 2400 / 70 correct option : a	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs 840", "rs 320", "rs 810", "rs 680" ] }	[ "C" ]	if 4 men working 10 hours a day earn rs . 600 per week , then 9 men working 6 hours a day will earn how much per week ?	"explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 600 : x hence 4 * 10 * x = 9 * 6 * 600 or x = 9 * 6 * 600 / 4 * 10 = 810 answer : c"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1", "10", "11", "19" ] }	[ "A" ]	the maximum number of student amoung them 1802 pens and 1203 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :	solution required number of student = h . c . f of 1802 and 1203 = 1 . answer a	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "95", "99", "26", "73" ] }	[ "D" ]	what two - digit number is less than the sum of the square of its digits by 15 and exceeds their doubled product by 5 ?	"let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 15 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 15 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . ...	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4", "5", "6", "12" ] }	[ "A" ]	suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 10 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?	"the part of job that suresh completes in 9 hours = 9 ⁄ 15 = 3 ⁄ 5 remaining job = 1 - 3 ⁄ 5 = 2 ⁄ 5 remaining job can be done by ashutosh in 2 ⁄ 5 × 10 = 4 hours answer a"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "3", "5", "7", "9" ] }	[ "A" ]	what least number must be subtracted from 427398 so that remaining number is divisible by 15	"explanation : on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted answer : option a"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 22000", "rs . 24000", "rs . 26000", "rs . 27000" ] }	[ "D" ]	sahil purchased a machine at rs 12000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .	"explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 12000 + 5000 + 1000 = 18000 150 % of 18000 = 150 / 100 * 18000 = 27000 option d"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1691100843", "4591100843", "4691100843", "3691100843" ] }	[ "C" ]	469157 * 9999	"explanation : 469157 * ( 10000 - 1 ) = 4691570000 - 469157 = 4691100843 option c"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "100", "200", "300", "400" ] }	[ "A" ]	in a partnership , a invests 1 ⁄ 6 of the capital for 1 ⁄ 6 of the time , b invests 1 ⁄ 3 of the capital for 1 ⁄ 3 of the time and c , the rest of the capital for whole time . find a ’ s share of the total profit of 2300	remaining capital = 1 - ( 1 ⁄ 6 + 1 ⁄ 3 ) = 1 ⁄ 2 ratio of their profit = 1 ⁄ 6 × [ 1 ⁄ 6 × 12 ] : 1 ⁄ 3 × [ 1 ⁄ 3 × 12 ] : 1 ⁄ 2 × 12 = 1 ⁄ 3 : 4 ⁄ 3 : 6 = 1 : 4 : 18 ∴ a ' s share = 1 / 1 + 4 + 18 × 2300 = 100 answer a	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs 312", "rs 412", "rs 512", "rs 612" ] }	[ "D" ]	find compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually	explanation : please apply the formula amount = p ( 1 + r 100 ) nc . i . = amount - p answer : d	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "30 π", "45 π", "60 π", "90 π" ] }	[ "C" ]	the front wheels of a wagon are 2 π feet in circumference and the rear wheels are 3 π feet in circumference . when the front wheels have made 10 more revolutions than the rear wheels , how many feet has the wagon travelled ?	solution let the rear wheel make x revolutions . then , the front wheel makes ( x + 10 ) revolutions . ( x + 10 ) x 3 π = x × 2 π ‹ = › 3 x + 30 = 2 x ‹ = › x = 30 . distance travelled by the wagon = ( 2 π x 30 ) ft ‹ = › ( 60 π ) ft . answer c	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "269", "285", "300", "275" ] }	[ "D" ]	lcm of two numbers is 7700 and hcf is 11 . if one number is 308 then other number is	option d	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 8400", "rs . 11,900", "rs . 13,600", "rs . 14,700" ] }	[ "D" ]	a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35,000 , a receives	"solution : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 . = > 3 x = 36000 . = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . so a ' s share = rs . ( 35000 x 21 / 50 ) = rs . 14,700 . answer : option d"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "33.33 %", "100 %", "75 %", "66.66 %" ] }	[ "B" ]	if x is less than y by 50 % then y exceed x by :	"using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 50 ( 100 - 50 ) * 100 = 100 % answer : b"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 850", "rs . 860", "rs . 876", "rs . 886" ] }	[ "C" ]	the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 square feet , how much will it cost to paint outside of a cube having 8 feet each side .	"explanation : we will first calculate the surface area of cube , then we will calculate the quantity of paint required to get answer . here we go , surface area = 6 a 2 = 6 ∗ 8 ( 2 ) = 384 sq feet quantity required = 38416 = 24 kg cost of painting = 36.50 ∗ 24 = rs . 876 option c"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "17 %", "20 %", "25 %", "30 %" ] }	[ "A" ]	if the price of sugar rises from rs . 10 per kg to rs . 12 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by	"sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x × 12 = x = 83 kg . ∴ reduction in consumption = 17 % . answer a"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "237.5", "234", "289.5", "345" ] }	[ "A" ]	jaclyn buys $ 10 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter	explanation : i = ( p x r x t ) / 100 = 10000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 237.5 answer : a	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 48.66", "rs . 51.03", "rs . 54.17", "rs . 55.33" ] }	[ "A" ]	if 10 litres of an oil of rs . 40 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ?	"40 * 10 = 400 66 * 5 = 330 730 / 15 = 48.66 answer : a"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 36", "rs . 72", "rs . 48", "rs . 96" ] }	[ "D" ]	the present worth of a sum due sometime hence is rs . 576 and the banker ’ s gain is rs . 16 . the true discount is	solution t . d = √ p . w xb . g = √ 576 x 16 = 96 . answer d	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4 m', '", "3 m', '", "2 m', '", "1 m', '" ] }	[ "C" ]	a rectangular plot 15 m × 10 m , has a path of grass outside it . if the area of grassy pathway is 54 m 2 , find the width of the path .	let the width of the path = w m then , length of plot with path = ( 15 + 2 w ) m and breadth of plot with path = ( 10 + 2 w ) m therefore , area of rectangular plot ( without path ) = 15 × 10 = 150 m 2 and area of rectangular plot ( with path ) = 150 + 54 = 204 m 2 hence , ( 15 + 2 w ) × ( 10 + 2 w ) = 204 ⇒ 4 w 2 + 50...	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 610", "rs . 612", "rs . 614", "rs . 616" ] }	[ "B" ]	find the compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually .	"explanation : amount = [ 7500 × ( 1 + 4100 ) 2 ] = ( 7500 × 2625 × 2625 ) = 8112 so compound interest = ( 8112 - 7500 ) = 612 answer : b"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 1200", "rs . 1500", "rs . 1800", "rs . 2000" ] }	[ "C" ]	a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3000 , a will get :	"explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 120 so , a ’ s amount = 120 × 15 = rs . 1800 . answer : option c"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 22941.18", "rs . 32941.18", "rs . 52941.18", "rs . 62941.18" ] }	[ "C" ]	a man sells a car to his friend at 15 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :	"explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 15 % . now s . p = rs . 45000 and loss = 15 % c . p . rs . [ 100 / 85 ã — 45000 ] = rs . 52941.18 correct option : c"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 200", "rs . 350", "rs . 475", "rs . 425" ] }	[ "C" ]	the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 225 , then the mean profit for the last 15 days would be	"average would be : 350 = ( 225 + x ) / 2 on solving , x = 475 . answer : c"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "462", "674", "672", "960" ] }	[ "A" ]	in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1100 employees , then the no . of female employees who are computer literate ?	"solution : total employees , = 1100 female employees , 60 % of 1100 . = ( 60 * 1100 ) / 100 = 660 . then male employees , = 440 50 % of male are computer literate , = 220 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1100 ) / 100 = 682 computer literate . thus , female computer lite...	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1260", "1320", "1200", "1250" ] }	[ "A" ]	what is the compound interest paid on a sum of rs . 6000 for the period of 2 years at 10 % per annum .	solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 6000 = 6000 * ( 21 / 100 ) = 1260 answer a	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4 / 7", "5 / 9", "2 / 3", "10 / 11" ] }	[ "C" ]	if 1 is added to the denominator of fraction , the fraction becomes 1 / 2 . if 1 is added to the numerator , the fraction becomes 1 . the fraction is	explanation : let the required fraction be a / b . then ⇒ a / b + 1 = 1 / 2 ⇒ 2 a – b = 1 - - - - ( 1 ) ⇒ a + 1 / b = 1 ⇒ a – b = – 1 ⇒ a – b = – 1 - - - - - - - ( 2 ) solving ( 1 ) & ( 2 ) we get a = 2 , b = 3 fraction = a / b = 2 / 3 correct option : c	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "32 m 3", "31.4 m 3", "40 m 3", "44 m 3" ] }	[ "B" ]	a circular well with a diameter of 2 metres , is dug to a depth of 10 metres . what is the volume of the earth dug out ?	"solution volume = π r 2 h ‹ = › ( 22 / 7 × 1 × 1 × 10 ) m 3 ‹ = › 31.4 m 3 . answer b"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 2000", "rs . 10,000", "rs . 15,000", "rs . 20,000" ] }	[ "D" ]	a man took a loan from a bank at the rate of 9 % 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 :	"solution principal = rs . ( 100 x 5400 / 9 x 3 ) = rs . 20000 . answer d"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "44 %", "120 %", "156 %", "40 %" ] }	[ "C" ]	if the radius of a circle is increased by 60 % then the area is increased by :	"initially a = pi * r 2 now r 2 = 160 / 100 r then area = pi * ( 160 r / 100 ) 2 area = 256 r / 100 that is area increases from 100 to 256 = increase in area = 156 % answer : c"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "35.2", "32.5", "36.5", "39.1" ] }	[ "B" ]	the mean of 50 observations was 32 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is	"sol . therefore correct sum = ( 32 × 50 + 48 – 23 ) = 1625 . therefore correct mean = 1625 / 50 = 32.5 . answer b"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "20 %", "25 %", "18 %", "30 %" ] }	[ "A" ]	if the given two numbers are respectively 5 % and 25 % of a third number , then what percentage is the first of the second ?	"here , l = 5 and m = 25 therefore , first number = l / m x 100 % of second number = 5 / 25 x 100 % of second number = 20 % of second number answer : a"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "70", "72", "75", "78" ] }	[ "D" ]	the average expenditure of a labourer for 6 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is	"income of 6 months = ( 6 × 85 ) – debt = 510 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 780 average monthly income = 780 ÷ 10 = 78 answer d"	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "22", "24", "26", "28" ] }	[ "C" ]	if 9 engines consume 24 metric tonnes of coal , when each is working 8 hoursday , bow much coal will be required for 8 engines , each running 13 hours a day , it being given that 3 engines of former type consume as much as 4 engines of latter type ?	let 3 engines of former type consume 1 unit in 1 hour . then , 4 engines of latter type consume 1 unit in 1 hour . therefore 1 engine of former type consumes ( 1 / 3 ) unit in 1 hour . 1 engine of latter type consumes ( 1 / 4 ) unit in 1 hour . let the required consumption of coal be x units . less engines , less coal ...	MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1 : 2", "3 : 5", "4 : 5", "16 : 15" ] }	[ "A" ]	a man invests some money partly in 10 % stock at 90 and partly in 5 % stock at 90 . to obtain equal dividends from both , he must invest the money in the ratio :	"solution for an income of rs . 1 in 10 % stock at 90 , investment = rs . ( 90 / 10 ) = rs . 9 . for an income of rs . 1 in 5 % stock at 90 , investment = rs . ( 90 / 5 ) = rs . 18 . ∴ ratio of investments = 9 : 18 = 1 : 2 answer a"	MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "6 , 8", "9 , 12", "12 , 16", "16 , 20" ] }

[ "A" ]

two numbers are such that the square of one is 224 less than 8 times the square of the other . if the numbers be in the ratio of 3 : 4 , the numbers are

solution let the numbers be 3 x and 4 x . then , ( 4 x ) 2 = 8 x ( 3 x ) 2 - 224 ‹ = › 16 x 2 = 72 x 2 - 224 ‹ = › 56 x 2 = 224 . ‹ = › x 2 = 4 . ‹ = › x = 2 . so , the numbers are 6 and 8 . answer a

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "750", "400", "800", "850" ] }

[ "B" ]

in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 160 vote ’ s majority . what is the total number of votes polled ?

"explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 160 ( 40 * 4 = 160 ) 100 % - - - - - > 400 ( 100 * 4 = 400 ) answer : option b"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "1865113", "1775123", "1764613", "1675123" ] }

[ "C" ]

( 4300231 ) - ? = 2535618

"let 4300231 - x = 2535618 then x = 4300231 - 2535618 = 1764613 answer is c"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "34", "25", "48", "50" ] }

[ "A" ]

the average of 40 results is 30 and the average of other 30 results is 40 . what is the average of all the results ?

answer sum of 70 result = sum of 40 result + sum of 30 result . = 40 x 30 + 30 x 40 = 2400 / 70 correct option : a

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "rs 840", "rs 320", "rs 810", "rs 680" ] }

[ "C" ]

if 4 men working 10 hours a day earn rs . 600 per week , then 9 men working 6 hours a day will earn how much per week ?

"explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 600 : x hence 4 * 10 * x = 9 * 6 * 600 or x = 9 * 6 * 600 / 4 * 10 = 810 answer : c"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "1", "10", "11", "19" ] }

[ "A" ]

the maximum number of student amoung them 1802 pens and 1203 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :

solution required number of student = h . c . f of 1802 and 1203 = 1 . answer a

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "95", "99", "26", "73" ] }

[ "D" ]

what two - digit number is less than the sum of the square of its digits by 15 and exceeds their doubled product by 5 ?

"let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 15 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 15 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . ...

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "4", "5", "6", "12" ] }

[ "A" ]

suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 10 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?

"the part of job that suresh completes in 9 hours = 9 ⁄ 15 = 3 ⁄ 5 remaining job = 1 - 3 ⁄ 5 = 2 ⁄ 5 remaining job can be done by ashutosh in 2 ⁄ 5 × 10 = 4 hours answer a"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "3", "5", "7", "9" ] }

[ "A" ]

what least number must be subtracted from 427398 so that remaining number is divisible by 15

"explanation : on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted answer : option a"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 22000", "rs . 24000", "rs . 26000", "rs . 27000" ] }

[ "D" ]

sahil purchased a machine at rs 12000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .

"explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 12000 + 5000 + 1000 = 18000 150 % of 18000 = 150 / 100 * 18000 = 27000 option d"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "1691100843", "4591100843", "4691100843", "3691100843" ] }

[ "C" ]

469157 * 9999

"explanation : 469157 * ( 10000 - 1 ) = 4691570000 - 469157 = 4691100843 option c"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "100", "200", "300", "400" ] }

[ "A" ]

in a partnership , a invests 1 ⁄ 6 of the capital for 1 ⁄ 6 of the time , b invests 1 ⁄ 3 of the capital for 1 ⁄ 3 of the time and c , the rest of the capital for whole time . find a ’ s share of the total profit of 2300

remaining capital = 1 - ( 1 ⁄ 6 + 1 ⁄ 3 ) = 1 ⁄ 2 ratio of their profit = 1 ⁄ 6 × [ 1 ⁄ 6 × 12 ] : 1 ⁄ 3 × [ 1 ⁄ 3 × 12 ] : 1 ⁄ 2 × 12 = 1 ⁄ 3 : 4 ⁄ 3 : 6 = 1 : 4 : 18 ∴ a ' s share = 1 / 1 + 4 + 18 × 2300 = 100 answer a

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "rs 312", "rs 412", "rs 512", "rs 612" ] }

[ "D" ]

find compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually

explanation : please apply the formula amount = p ( 1 + r 100 ) nc . i . = amount - p answer : d

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "30 π", "45 π", "60 π", "90 π" ] }

[ "C" ]

the front wheels of a wagon are 2 π feet in circumference and the rear wheels are 3 π feet in circumference . when the front wheels have made 10 more revolutions than the rear wheels , how many feet has the wagon travelled ?

solution let the rear wheel make x revolutions . then , the front wheel makes ( x + 10 ) revolutions . ( x + 10 ) x 3 π = x × 2 π ‹ = › 3 x + 30 = 2 x ‹ = › x = 30 . distance travelled by the wagon = ( 2 π x 30 ) ft ‹ = › ( 60 π ) ft . answer c

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "269", "285", "300", "275" ] }

[ "D" ]

lcm of two numbers is 7700 and hcf is 11 . if one number is 308 then other number is

option d

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 8400", "rs . 11,900", "rs . 13,600", "rs . 14,700" ] }

[ "D" ]

a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35,000 , a receives

"solution : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 . = > 3 x = 36000 . = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . so a ' s share = rs . ( 35000 x 21 / 50 ) = rs . 14,700 . answer : option d"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "33.33 %", "100 %", "75 %", "66.66 %" ] }

[ "B" ]

if x is less than y by 50 % then y exceed x by :

"using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 50 ( 100 - 50 ) * 100 = 100 % answer : b"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 850", "rs . 860", "rs . 876", "rs . 886" ] }

[ "C" ]

the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 square feet , how much will it cost to paint outside of a cube having 8 feet each side .

"explanation : we will first calculate the surface area of cube , then we will calculate the quantity of paint required to get answer . here we go , surface area = 6 a 2 = 6 ∗ 8 ( 2 ) = 384 sq feet quantity required = 38416 = 24 kg cost of painting = 36.50 ∗ 24 = rs . 876 option c"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "17 %", "20 %", "25 %", "30 %" ] }

[ "A" ]

if the price of sugar rises from rs . 10 per kg to rs . 12 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by

"sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x × 12 = x = 83 kg . ∴ reduction in consumption = 17 % . answer a"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "237.5", "234", "289.5", "345" ] }

[ "A" ]

jaclyn buys $ 10 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter

explanation : i = ( p x r x t ) / 100 = 10000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 237.5 answer : a

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 48.66", "rs . 51.03", "rs . 54.17", "rs . 55.33" ] }

[ "A" ]

if 10 litres of an oil of rs . 40 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ?

"40 * 10 = 400 66 * 5 = 330 730 / 15 = 48.66 answer : a"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 36", "rs . 72", "rs . 48", "rs . 96" ] }

[ "D" ]

the present worth of a sum due sometime hence is rs . 576 and the banker ’ s gain is rs . 16 . the true discount is

solution t . d = √ p . w xb . g = √ 576 x 16 = 96 . answer d

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "4 m', '", "3 m', '", "2 m', '", "1 m', '" ] }

[ "C" ]

a rectangular plot 15 m × 10 m , has a path of grass outside it . if the area of grassy pathway is 54 m 2 , find the width of the path .

let the width of the path = w m then , length of plot with path = ( 15 + 2 w ) m and breadth of plot with path = ( 10 + 2 w ) m therefore , area of rectangular plot ( without path ) = 15 × 10 = 150 m 2 and area of rectangular plot ( with path ) = 150 + 54 = 204 m 2 hence , ( 15 + 2 w ) × ( 10 + 2 w ) = 204 ⇒ 4 w 2 + 50...

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 610", "rs . 612", "rs . 614", "rs . 616" ] }

[ "B" ]

find the compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually .

"explanation : amount = [ 7500 × ( 1 + 4100 ) 2 ] = ( 7500 × 2625 × 2625 ) = 8112 so compound interest = ( 8112 - 7500 ) = 612 answer : b"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 1200", "rs . 1500", "rs . 1800", "rs . 2000" ] }

[ "C" ]

a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3000 , a will get :

"explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 120 so , a ’ s amount = 120 × 15 = rs . 1800 . answer : option c"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 22941.18", "rs . 32941.18", "rs . 52941.18", "rs . 62941.18" ] }

[ "C" ]

a man sells a car to his friend at 15 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :

"explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 15 % . now s . p = rs . 45000 and loss = 15 % c . p . rs . [ 100 / 85 ã — 45000 ] = rs . 52941.18 correct option : c"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 200", "rs . 350", "rs . 475", "rs . 425" ] }

[ "C" ]

the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 225 , then the mean profit for the last 15 days would be

"average would be : 350 = ( 225 + x ) / 2 on solving , x = 475 . answer : c"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "462", "674", "672", "960" ] }

[ "A" ]

in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1100 employees , then the no . of female employees who are computer literate ?

"solution : total employees , = 1100 female employees , 60 % of 1100 . = ( 60 * 1100 ) / 100 = 660 . then male employees , = 440 50 % of male are computer literate , = 220 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1100 ) / 100 = 682 computer literate . thus , female computer lite...

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "1260", "1320", "1200", "1250" ] }

[ "A" ]

what is the compound interest paid on a sum of rs . 6000 for the period of 2 years at 10 % per annum .

solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 6000 = 6000 * ( 21 / 100 ) = 1260 answer a

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "4 / 7", "5 / 9", "2 / 3", "10 / 11" ] }

[ "C" ]

if 1 is added to the denominator of fraction , the fraction becomes 1 / 2 . if 1 is added to the numerator , the fraction becomes 1 . the fraction is

explanation : let the required fraction be a / b . then ⇒ a / b + 1 = 1 / 2 ⇒ 2 a – b = 1 - - - - ( 1 ) ⇒ a + 1 / b = 1 ⇒ a – b = – 1 ⇒ a – b = – 1 - - - - - - - ( 2 ) solving ( 1 ) & ( 2 ) we get a = 2 , b = 3 fraction = a / b = 2 / 3 correct option : c

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "32 m 3", "31.4 m 3", "40 m 3", "44 m 3" ] }

[ "B" ]

a circular well with a diameter of 2 metres , is dug to a depth of 10 metres . what is the volume of the earth dug out ?

"solution volume = π r 2 h ‹ = › ( 22 / 7 × 1 × 1 × 10 ) m 3 ‹ = › 31.4 m 3 . answer b"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 2000", "rs . 10,000", "rs . 15,000", "rs . 20,000" ] }

[ "D" ]

a man took a loan from a bank at the rate of 9 % 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 :

"solution principal = rs . ( 100 x 5400 / 9 x 3 ) = rs . 20000 . answer d"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "44 %", "120 %", "156 %", "40 %" ] }

[ "C" ]

if the radius of a circle is increased by 60 % then the area is increased by :

"initially a = pi * r 2 now r 2 = 160 / 100 r then area = pi * ( 160 r / 100 ) 2 area = 256 r / 100 that is area increases from 100 to 256 = increase in area = 156 % answer : c"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "35.2", "32.5", "36.5", "39.1" ] }

[ "B" ]

the mean of 50 observations was 32 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is

"sol . therefore correct sum = ( 32 × 50 + 48 – 23 ) = 1625 . therefore correct mean = 1625 / 50 = 32.5 . answer b"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "20 %", "25 %", "18 %", "30 %" ] }

[ "A" ]

if the given two numbers are respectively 5 % and 25 % of a third number , then what percentage is the first of the second ?

"here , l = 5 and m = 25 therefore , first number = l / m x 100 % of second number = 5 / 25 x 100 % of second number = 20 % of second number answer : a"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "70", "72", "75", "78" ] }

[ "D" ]

the average expenditure of a labourer for 6 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is

"income of 6 months = ( 6 × 85 ) – debt = 510 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 780 average monthly income = 780 ÷ 10 = 78 answer d"

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "22", "24", "26", "28" ] }

[ "C" ]

if 9 engines consume 24 metric tonnes of coal , when each is working 8 hoursday , bow much coal will be required for 8 engines , each running 13 hours a day , it being given that 3 engines of former type consume as much as 4 engines of latter type ?

let 3 engines of former type consume 1 unit in 1 hour . then , 4 engines of latter type consume 1 unit in 1 hour . therefore 1 engine of former type consumes ( 1 / 3 ) unit in 1 hour . 1 engine of latter type consumes ( 1 / 4 ) unit in 1 hour . let the required consumption of coal be x units . less engines , less coal ...

MathQA

{ "label": [ "A", "B", "C", "D" ], "text": [ "1 : 2", "3 : 5", "4 : 5", "16 : 15" ] }

[ "A" ]

a man invests some money partly in 10 % stock at 90 and partly in 5 % stock at 90 . to obtain equal dividends from both , he must invest the money in the ratio :

"solution for an income of rs . 1 in 10 % stock at 90 , investment = rs . ( 90 / 10 ) = rs . 9 . for an income of rs . 1 in 5 % stock at 90 , investment = rs . ( 90 / 5 ) = rs . 18 . ∴ ratio of investments = 9 : 18 = 1 : 2 answer a"

MathQA