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": [
"4000",
"24000",
"8000",
"10000"
]
} | [
"B"
] | a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 15 % on conveyance . if his savings at the end of the month is rs . 1200 , then his salary per month in rupees is : | "total expenditure = 40 + 25 + 15 + 15 = 95 % saving = ( 100 - 95 ) = 5 % 5 / 100 × salary = 1200 , salary = 24000 rs . answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"9 : 16",
"5 : 9",
"12 : 17",
"13 : 24"
]
} | [
"A"
] | find the ratio between 1 hr 30 minutes and 2 hrs 40 minutes . | solution : the ratio = 1 hr 30 min : 2 hr 40 min . 90 min : 160 min = 9 : 16 . answer is a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"276",
"299",
"312",
"460"
]
} | [
"D"
] | the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 21 and 23 . the larger of the two numbers is | "solution clearly , the numbers are ( 20 x 21 ) and ( 20 x 23 ) . larger number = ( 20 x 23 ) = 460 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 480",
"rs . 520",
"rs . 600",
"rs . 960"
]
} | [
"C"
] | the banker ' s gain of a certain sum due 2 years hence at 10 % per annum is rs . 24 . the present worth is | solution t . d = ( b . g x 100 / rate x time ) = rs . ( 24 x 100 / 10 x 2 ) = rs . 120 . p . w = ( 100 x t . d / rate x time ) = rs . ( 100 x 120 / 10 x 2 ) = rs . 600 . answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4000",
"6000",
"4400",
"4500"
]
} | [
"B"
] | if 10 % of 30 % of 50 % of a number is 90 , then what is the number ? | "let the number be a given , 10 / 100 * 30 / 100 * 50 / 100 * a = 90 = > 1 / 10 * 3 / 10 * 1 / 2 * a = 90 = > a = 10 * 20 * 10 * 2 = 6000 . answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"74 kg",
"76.5 kg",
"85 kg",
"78"
]
} | [
"A"
] | the average weight of 2 person ' s increases by 4.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? | "explanation : total weight increased = ( 2 x 4.5 ) kg = 9 kg . weight of new person = ( 65 + 9 ) kg = 74 kg . answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"14",
"16",
"19",
"21"
]
} | [
"B"
] | if the sum of a number and its square is 272 , what is the number ? | "explanation : let the integer be x . then , x + x 2 = 272 x 2 + x - 272 = 0 ( x + 17 ) ( x – 16 ) = 0 x = 16 answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18 %",
"20 %",
"21 %",
"23 %"
]
} | [
"D"
] | two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 30 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of | answer : d . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 %",
"9 %",
"11.11 %",
"12 %"
]
} | [
"C"
] | a shopkeeper forced to sell at cost price , uses a 900 grams weight for a kilogram . what is his gain percent ? | "shopkeeper sells 900 g instead of 1000 g . so , his gain = 1000 - 900 = 100 g . thus , % gain = ( 100 * 100 ) / 900 = 11.11 % . answer : option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"22.8 kg",
"25.6 kg",
"28 kg",
"30.4 kg"
]
} | [
"D"
] | if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 8 m of the same rod ? | explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 8 : : 42.75 : x = > 11.25 x x = 8 x 42.75 = > x = ( 8 x 42.75 ) / 11.25 = > x = 30.4 answer : d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"70",
"125",
"300",
"500"
]
} | [
"A"
] | the radius of the wheel of a bus is 250 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is | "radius of the wheel of bus = 250 cm . then , circumference of wheel = 2 ï € r = 500 ï € = 1571.43440 cm distance covered by bus in 1 minute = 66 â „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 1571.45 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 1571.43 = 70 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"55",
"56",
"57",
"52"
]
} | [
"D"
] | a rectangular plot measuring 90 metres by 40 metres is to be enclosed by wire fencing . if the poles of the fence are kept 5 metres apart , how many poles will be needed ? | "solution perimeter of the plot = 2 ( 90 + 40 ) = 260 m . ∴ number of poles = [ 260 / 5 ] = 52 m answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"31",
"36",
"53",
"58"
]
} | [
"C"
] | the average age of 38 students in a group is 14 years . when teacher â € ™ s age is included to it , the average increases by one . what is the teacher â € ™ s age in years ? | "sol . age of the teacher = ( 39 ã — 15 â € “ 38 ã — 14 ) years = 53 years . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4.37 %",
"5 %",
"3 %",
"8.75 %"
]
} | [
"C"
] | the population of a town increased from 1 , 75,000 to 2 , 27,500 in a decade . the average percent increase of population per year is | "solution increase in 10 years = ( 227500 - 175000 ) = 52500 . increase % = ( 52500 / 175000 ã — 100 ) % = 30 % . required average = ( 30 / 10 ) % = 3 % . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"- 1466",
"2801",
"- 2801",
"- 2071"
]
} | [
"A"
] | - 54 x 29 + 100 = ? | given exp . = - 54 x ( 30 - 1 ) + 100 = - ( 54 x 30 ) + 54 + 100 = - 1620 + 154 = - 1466 answer is a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2520",
"1800",
"2700",
"10800"
]
} | [
"A"
] | running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 14 such machines produce in 4 minutes ? | "solution let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) â ˆ ´ 6 ã — 1 ã — x = 14 ã — 4 ã — 270 â ‡ ” x = 14 x 4 x 270 / 6 = 2520 . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"325",
"425",
"625",
"700"
]
} | [
"C"
] | there are 250 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers . | as per question stem 2 / 5 m ( portion of men employees who are managers ) + 250 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 250 = 2 / 5 t , or 2 / 5 ( t - m ) = 250 , from here we get that t - m = 625 , that would be total number of female employees and the answer ( c ) | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"66",
"74",
"78",
"98"
]
} | [
"D"
] | ashok secured average of 78 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ? | "explanation : number of subjects = 6 average of marks in 6 subjects = 78 therefore total marks in 6 subjects = 78 * 6 = 468 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 468 – 370 = 98 answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7.5 hr",
"8 hr",
"8.57 hr",
"10 hr"
]
} | [
"C"
] | two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 15 hr . if all pipes are opened simultaneously , then the cistern will be filled in | "solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 15 = 7 / 60 hence , tank will be filled in 60 / 7 = 8.57 hour option ( c )" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 840",
"rs 1350",
"rs 1620",
"rs 1680"
]
} | [
"B"
] | if 4 men working 10 hours a day earn rs . 1000 per week , then 9 men working 6 hours a day will earn how much per week ? | explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1000 : x hence 4 * 10 * x = 9 * 6 * 1000 or x = 9 * 6 * 1000 / 4 * 10 = 1350 answer : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"121",
"3267",
"363",
"33"
]
} | [
"C"
] | if both 112 and 33 are factors of the number a * 43 * 62 * 1311 , then what is the smallest possible value of a ? | explanatory answer step 1 : prime factorize the given expression a * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311 step 2 : find factors missing after excluding ' a ' to make the number divisible by both 112 and 33 112 is a factor of the given number . if we do not include ' a ' , 11 is not a prime factor of the given number . if 112 is a factor of the number , 112 should have been in ' a ' 33 is a factor of the given number . if we do not include ' a ' , the number has only 32 in it . therefore , if 33 has to be a factor of the given number ' a ' has to contain 31 in it . therefore , ' a ' should be at least 112 * 3 = 363 if the given number has 112 and 33 as its factors . the smallest value that ` ` a ' ' can take is 363 . choice c is the correct answer . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 %",
"50 %",
"21.4 %",
"52 %"
]
} | [
"C"
] | a retailer buys a radio for rs 232 . his overhead expenses are rs 15 . he sellis the radio for rs 300 . the profit percent of the retailer is | explanation : cost price = ( 232 + 15 ) = 247 sell price = 300 gain = ( 53 / 247 ) * 100 = 21.4 % . answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"60",
"45",
"20",
"15"
]
} | [
"B"
] | a ratio between two numbers is 3 : 4 and their l . c . m . is 180 . the first number is | "sol . let the required numbers be 3 x and 4 x . then , their l . c . m . is 12 x . ∴ 12 x = 180 ⇔ x = 15 . hence , the first number is 45 . answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7.2 kg .",
"10.8 kg .",
"12.4 kg .",
"6.18 kg"
]
} | [
"D"
] | if the weight of 13 meters long rod is 13.4 kg . what is the weight of 6 meters long rod ? | answer ∵ weight of 13 m long rod = 13.4 kg ∴ weight of 1 m long rod = 13.4 / 13 kg ∴ weight of 6 m long rod = 13.4 x 6 / 13 = 6.18 kg option : d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"13 %",
"18 %",
"36 %",
"64 %"
]
} | [
"A"
] | if the area of a circle decreases by 25 % , then the radius of a circle decreases by | "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 25 ) % = ( 100 − 10 √ 75 ) % = 100 - 87 = 13 % answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"11 : 9",
"11 : 18",
"21 : 19",
"21 : 19"
]
} | [
"A"
] | the sum of two numbers is 40 and their difference is 4 . the ratio of the numbers is | sol . let the numbers be x and y . then , x + y / x - y = 40 / 4 = 10 ⇔ ( x + y ) = 10 ( x - y ) ⇔ 9 x = 11 y ⇔ x / y = 11 / 9 . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"33.33 m",
"25 m",
"45 m",
"30 m"
]
} | [
"A"
] | in a 100 m race , a covers the distance in 30 seconds and b in 45 second . in this race a beats b by : | solution distance covered by b in 15 sec . = ( 100 / 45 x 15 ) m = 33.33 m . ∴ a beats b by 33.33 metres . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 7500",
"rs . 9000",
"rs . 9500",
"rs . 10,000"
]
} | [
"A"
] | a and b started a business in partnership investing rs . 20000 and rs . 15000 respectively . after 6 months , c joined them with rs . 20000 . what will be b ' s share in the total profit of rs . 25000 earned at the end of 2 years from the starting of the business ? | solution a : b : c = ( 20000 × 24 ) : ( 15000 × 24 ) : ( 20000 × 18 ) = 4 : 3 : 3 b ' s share = rs . ( 25000 × 3 / 10 ) = rs . 7500 . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2574",
"2500",
"1365",
"1574"
]
} | [
"A"
] | if the product of two numbers is 84942 and their h . c . f . is 33 , find their l . c . m . | "explanation : hcf * lcm = 84942 , because we know product of two numbers = product of hcf and lcm lcm = 84942 / 33 = 2574 option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"75 m .",
"128 m .",
"150 m .",
"100 m ."
]
} | [
"B"
] | a runs twice as fast as b and gives b a start of 64 m . how long should the racecourse be so that a and b might reach in the same time ? | "ratio of speeds of a and b is 2 : 1 b is 64 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 64 m is 64 / 1 = 64 m so the total time taken by a and b to reach = 2 * 64 = 128 m answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10",
"100",
"1000",
"10000"
]
} | [
"B"
] | ( 1000 ) 7 ÷ ( 10 ) 19 = ? | "explanation : = ( 103 ) 7 / ( 10 ) 19 = ( 10 ) 21 / ( 10 ) 19 = 10 ( 2 ) = 100 option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 165.50",
"rs . 1700",
"rs . 175.50",
"rs . 180"
]
} | [
"A"
] | tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 143 per kg , the price of the third variety per kg will be | "solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 143 / 22.50 = 1 = â € º x - 143 = 22.50 = â € º x = 165.50 . hence , price of the third variety = rs . 165.50 per kg . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 7000",
"rs . 8000",
"rs . 8500",
"rs . 9000"
]
} | [
"D"
] | the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 16000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is | "answer average salary = 8000 + 5000 + 16000 + 7000 + 9000 / 5 = rs . 9000 correct option : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1.2",
"4.8",
"4.4",
"3.21"
]
} | [
"B"
] | the simple interest on rs . 8 for 12 months at the rate of 5 paise per rupeeper month is | "sol . s . i . = rs . [ 8 * 5 / 100 * 12 ] = rs . 4.8 answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7 %",
"9 %",
"11 %",
"12 %"
]
} | [
"B"
] | if 12 % of x is equal to 6 % of y , then 18 % of x will be equal to how much % of y ? | we have , 12 % of x = 6 % of y = > 2 % of x = 1 % of y = > ( 2 x 9 ) % of x = ( 1 x 9 ) % of y thus , 18 % of x = 9 % of y . answer : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12.75",
"50",
"85",
"204"
]
} | [
"C"
] | the difference between a number and its two fifth is 510 . what is 10 % of that number ? | "solution let the number be x . then , x - 2 / 5 x = 510 . ‹ = › 3 / 5 x = 510 ‹ = › x = [ 510 x 5 / 3 ] = 850 . therefore 10 % of 850 = 85 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20",
"40",
"60",
"80"
]
} | [
"A"
] | the maximum number of student amoung them 1020 pens and 860 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 1020 and 860 = 20 . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"144",
"288",
"12",
"256"
]
} | [
"A"
] | in how many ways 4 boys and 3 girls can be seated in a row so that they are alternate . | "solution : let the arrangement be , b g b g b g b 4 boys can be seated in 4 ! ways . girl can be seated in 3 ! ways . required number of ways , = 4 ! * 3 ! = 144 . answer : option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"250",
"276",
"280",
"310"
]
} | [
"D"
] | a library has an average of 660 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is : | "since the month begins with sunday , to there will be five sundays in the month average required = ( 660 x 5 + 240 x 25 ) / 30 ) = 310 answer : option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"17",
"39",
"42",
"45"
]
} | [
"A"
] | a batsman makes a score of 65 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning . | let the average after 17 th inning = x . then , average after 16 th inning = ( x – 3 ) . ∴ 16 ( x – 3 ) + 65 = 17 x or x = ( 65 – 48 ) = 17 . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"13 , 3",
"12 , 6",
"16 , 4",
"14 , 4"
]
} | [
"C"
] | a man can row downstream at 20 kmph and upstream at 12 kmph . find the speed of the man in still water and the speed of stream respectively ? | "explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 20 - - - ( 1 ) and x - y = 12 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 32 = > x = 16 , y = 4 . answer : option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"19",
"18",
"9.12",
"20"
]
} | [
"C"
] | tom read a book containing 560 pages by reading the same number of pages each day . if he would have finished the book 5 days earlier by reading 16 pages a day more , how many days did tom spend reading the book ? | "actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 560 ( we want to find the days , sop = 560 / d ) 2 ) ( p + 16 ) ( d - 5 ) = 560 = > pd - 5 p + 16 d - 80 = 560 as the 1 ) stated u can put 1 ) into 2 ) = > 560 - 5 p + 16 d - 80 = 560 = > 16 d - 5 p = 80 put the bold one into it = > 16 d - 5 ( 560 / d ) = 80 the we get the final equation 16 d ^ 2 - 2800 = 80 d ( divide 16 ) = > d ^ 2 - 5 d - 175 = 0 ( d - 15 ) ( d + 10 ) = 0 so d = 9.12 days ans : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"100', '",
"104', '",
"108', '",
"112', '"
]
} | [
"B"
] | a farmer built a fence around his square plot . he used 27 fence poles on each side of the square . how many poles did he need altogether ? | one side = 2 corners ( 1 nd 1 each ) plus 25 . . . 1 25 1 25 25 1 25 1 der 4 ans = 25 * 4 + 4 = 104 answer : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"- 4212",
"4601",
"- 4801",
"- 3471"
]
} | [
"A"
] | - 88 * 49 + 100 = ? | "= > - 88 * ( 50 - 1 ) + 100 ; = > - ( 88 * 50 ) + 88 + 100 ; = > - 4400 + 188 = - 4212 . correct option : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20 %",
"15 %",
"30 %",
"25 %"
]
} | [
"D"
] | if 25 % of ( x - y ) = 15 % of ( x + y ) , then what percent of x is y ? | "explanation : solution : 25 % of ( x - y ) = 15 % of ( x + y ) 25 ( x - y ) / 100 = 15 ( x + y ) / 100 5 ( x - y ) = 3 ( x + y ) x = 4 y . . ' . required percentage = ( y * 100 / x ) % = y * 100 / 4 y = 25 % answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4 ⁄ 5', '",
"3 ⁄ 5', '",
"5 ⁄ 6', '",
"6 ⁄ 7', '"
]
} | [
"A"
] | from a square piece of a paper having each side equal to 10 cm , the largest possible circle is being cut out . the ratio of the area of the circle to the area of the original square is nearly : | area of the square = ( 10 ) 2 = 100 cm 2 area of the circle = 22 ⁄ 7 × ( 5 ) 2 = 22 × 25 / 7 required ratio = 22 × 25 / 7 × 100 = 22 / 28 = 11 / 14 = 0.785 ≈ 0.8 = 4 ⁄ 5 answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10.6 kg",
"10.8 kg",
"11 kg",
"14.9 kg"
]
} | [
"C"
] | the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.8 kg . the weight of the new student is ? | answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.8 - 19 x 15 ) kg = 11 kg . correct option : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18 %",
"26.57 %",
"20 %",
"19 %"
]
} | [
"B"
] | mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 456 ? | "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 456 , discount = 621 - 456 = 165 discount % = 165 / 621 * 100 = 26.57 % answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"25 %",
"33.33 %",
"40 %",
"75 %"
]
} | [
"B"
] | a rectangle having length 100 cm and width 40 cm . if the length of the rectangle is increased by fifty percent then how much percent the breadth should be decreased so as to maintain the same area . | "explanation : solution : ( 50 / ( 100 + 50 ) * 100 ) % = 33.33 % answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"427",
"859",
"860",
"4320"
]
} | [
"C"
] | the least number which when increased by 4 each divisible by each one of 22 , 32 , 36 and 54 is : | "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 4 = 864 - 4 = 860 . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 80",
"rs . 185",
"rs . 140",
"rs . 295"
]
} | [
"C"
] | a trader sells 30 meters of cloth for rs . 4500 at the profit of rs . 10 per metre of cloth . what is the cost price of one metre of cloth ? | "sp of 1 m of cloth = 4500 / 30 = rs . 150 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 150 - rs . 10 = rs . 140 . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.07",
"0.9",
"9",
"90"
]
} | [
"A"
] | what is 15 % of 2 / 3 of 0.7 ? | "the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 7 / 10 ) = 210 / 3000 = 0.07 option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 : 2",
"2 : 3",
"3 : 4",
"3 : 8"
]
} | [
"C"
] | the ratio between sumit ' s and prakash ' s age at present is 2 : 3 . sumit is 6 years younger than prakash . the ratio of sumit ' s age to prakash ' s age after 6 years will be : | explanation : let their ages be 2 x and 3 x years . 3 x - 2 x = 6 or x = 6 sumit ' s age = 12 years , prakash ' s age = 24 years ratio of their ages = 18 : 24 = 3 : 4 . correct option : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 4082.40",
"rs . 1024.21",
"rs . 2810.6",
"rs . 3214"
]
} | [
"A"
] | an order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth . what be the cost of a carpet whose length and breadth are 40 % more and 25 % more respectively than the first carpet . given that the ratio of carpet is rs . 45 per sq . m ? | explanation : length of the first carpet = ( 1.44 ) ( 6 ) = 8.64 cm area of the second carpet = 8.64 ( 1 + 40 / 100 ) 6 ( 1 + 25 / 100 ) = 51.84 ( 1.4 ) ( 5 / 4 ) sq m = ( 12.96 ) ( 7 ) sq m cost of the second carpet = ( 45 ) ( 12.96 x 7 ) = 315 ( 13 - 0.04 ) = 4095 - 12.6 = rs . 4082.40 answer is a | MathQA |
{
"label": [
"A",
"B",
"C",
"E"
],
"text": [
"25 , 20",
"30 , 15",
"50 , 15",
"75,35"
]
} | [
"C"
] | find the side of the largest possible square slabs which can be paved on the floor of a room 2 m 50 cm long and 1 m 50 cm broad . also find the number of such slabs to pave the floor . | explanation : hcf ( 250 , 150 ) = 50 cm the number slabs = 250 * 150 / 50 * 50 = 15 answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 : 9', '",
"2 : 9', '",
"3 : 9', '",
"5 : 9', '"
]
} | [
"A"
] | two cubes have their volumes in the ratio 1 : 27 . find the ratio of their surface areas . | let their edges be a and b . then , = a ^ 3 / b ^ 3 = 1 / 27 ( or ) ( a / b ) ^ 3 = ( 1 / 3 ) 3 ( or ) ( a / b ) = ( 1 / 3 ) . therefore , ratio of their surface area = 6 a ^ 2 / 6 b ^ 2 = a ^ 2 / b ^ 2 = ( a / b ) ^ 2 = 1 / 9 , i . e . 1 : 9 . answer is a . | MathQA |
{
"label": [
"A",
"B",
"C",
"E"
],
"text": [
"400",
"500",
"505",
"506"
]
} | [
"B"
] | evaluate 35 / . 07 | "explanation : 35 / . 07 = 3500 / 7 = 500 option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"6420",
"8960",
"5120",
"4830"
]
} | [
"C"
] | a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corner , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is | "sol . clearly , l = ( 48 - 16 ) m = 32 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . ∴ volume of the box = ( 32 x 20 x 8 ) m 3 = 5120 m 3 answer c" | MathQA |
{
"label": [
"A",
"B",
"D",
"E"
],
"text": [
"1",
"2",
"- 1 / 2",
"- 1"
]
} | [
"B"
] | if | x | = 4 x - 2 , then x = ? | "answer : approach : substituted option a i . e x = 2 . inequality satisfied . b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"80 kmph",
"60 kmph",
"70 kmph",
"90 kmph"
]
} | [
"C"
] | a train travels 225 km in 3.5 hours and 370 km in 5 hours . find the average speed of train . | "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 225 + 370 = 595 km thus , total speed = 8.5 hrs or , average speed = 595 / 8.5 or , 70 kmph . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"51 : 52",
"52 : 54",
"53 : 54",
"54 : 55"
]
} | [
"B"
] | the cash difference between the selling prices of an article at a profit of 4 % and 8 % is rs 3 . the ratio of two selling prices is | "explanation : let the cost price of article is rs . x required ratio = ( 104 % of x ) / ( 108 % of x ) = 104 / 108 = 52 / 54 = 52 : 54 . answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3.5",
"2.75",
"4.25",
"4.5"
]
} | [
"A"
] | ( 17 ) 4.5 x ( 17 ) ? = 178 | "solution let ( 17 ) 4.5 * ( 17 ) x = 178 . then , ( 17 ) 4.5 + x = ( 17 ) 8 . ∴ 4.5 + x = 8 ⇔ x = ( 8 - 4.5 ) ⇔ x = 3.5 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20 min",
"35 min",
"50 min",
"70 min"
]
} | [
"C"
] | a can go round a circular path 8 times in 40 minutes . if the diameter of the circle is increased to 10 times the original diameter , then the time required by a to go round the new path once , travelling at the same speed as before is | solution let original diameter be d metres . then , its circumference = ( π d ) metres . time taken to cover ( 8 π d ) m = 40 min . new diameter = ( 10 d ) m . then , its circumference = ( π x 10 d ) m . time taken to go round it once ‹ = › [ 40 / 8 π d x 10 π d ] m ‹ = › 50 min . answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"5 %",
"6 %",
"8 %",
"10 %"
]
} | [
"B"
] | mukesh borrowed a sum of rs . 10000 at simple interest from a bank . after two years he takes rs . 12000 more as loan and discharge all the debt at the end of next 3 years depositing rs . 27160 to the bank . what is the rate of interest per annum ? | si = 27160 - ( principal amount ) = 27160 - 22000 = 5160 . now , ( 10000 * 5 * r / 100 ) + ( 12000 * 3 * r / 100 ) = 5160 . 500 r + 360 r = 5160 . . . . . rate = 6 % . answer : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1280",
"1270",
"1260",
"1250"
]
} | [
"A"
] | if to a certain number , 720 be added , and the sum be divided by 125 ; the quotient will be equal to 7392 divided by 462 . what is that number ? | solution let x = the number required . a = 720 d = 7392 b = 125 h = 462 then by the conditions of the problem ( x + a ) / b = d / h therefore x = ( bd - ah ) / h restoring the numbers , x = [ ( 125.7392 ) - ( 720.462 ) ] / 462 = 1280 . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"200",
"250",
"300",
"500"
]
} | [
"D"
] | the radius of the wheel of a bus is 35 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is | radius of the wheel of bus = 35 cm . then , circumference of wheel = 2 ï € r = 70 ï € = 220 cm distance covered by bus in 1 minute = 66 â „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 220 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 220 = 500 answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"36",
"52",
"66",
"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 : | "sol . t . d . = √ p . w . * b . g . = √ 576 * 16 = 96 . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4242",
"4155",
"1123",
"11023"
]
} | [
"B"
] | 7589 - ? = 3434 | "let 7589 - x = 3434 then x = 7589 - 3434 = 4155 answer is b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"750",
"700",
"900",
"850"
]
} | [
"C"
] | in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 360 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 % - - - - - > 360 ( 40 * 9 = 360 ) 100 % - - - - - > 900 ( 100 * 9 = 900 ) answer : option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"25 %",
"20 %",
"16.67 %",
"33.33 %"
]
} | [
"B"
] | if the price of petrol increases by 25 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ? | "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 25 ) i . e 125 . now , his consumption should be reduced to : - = 125 − 100125 ∗ 100 . hence , the consumption should be reduced to 20 % . answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4",
"5",
"6",
"12"
]
} | [
"C"
] | suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 15 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 â „ 15 = 3 â „ 5 remaining job = 1 - 3 â „ 5 = 2 â „ 5 remaining job can be done by ashutosh in 2 â „ 5 ã — 15 = 6 hours answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 750",
"rs . 1000",
"rs . 850",
"rs . 1250"
]
} | [
"D"
] | the ratio between the number of passengers travelling by i and ii class between the two railway stations is 1 : 50 , whereas the ratio of i and ii class fares between the same stations is 3 : 1 . if on a particular day rs . 1,325 were collected from the passengers travelling between these stations , then what was the amount collected from the ii class passengers ? | let x be the number of passengers and y be the fare taken from passengers . 3 xy + 50 xy = 1325 = > xy = 25 amount collected from ii class passengers = 25 × 50 = rs . 1250 . answer : d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"28000",
"30000",
"32000",
"35000"
]
} | [
"D"
] | a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 5000 as profit , what is their total profit ? | "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 5000 = > total profit = 5000 * 7 = 35000 . answer : option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18.38 %",
"20 %",
"25 %",
"50 %"
]
} | [
"A"
] | ritesh and co . generated revenue of rs . 1,700 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ? | "explanation : given , ritesh and co . generated revenue of rs . 1,700 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1700 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 1700 . = > 13,600 . hence , the total revenue by end of 2007 is rs . 13,600 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 13600 ) × 100 . = > 18.38 % . answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 14000",
"rs 15000",
"rs 16000",
"rs 17000"
]
} | [
"B"
] | a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 5400 interest . the principal amount borrowed by him was . | "explanation : s . i . = p ∗ r ∗ t / 100 = > p = s . i . ∗ 100 / r ∗ t = > p = 5400 ∗ 100 / 12 ∗ 3 = rs 15000 option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"24",
"25",
"48",
"50"
]
} | [
"C"
] | the average of 60 results is 40 and the average of other 40 results is 60 . what is the average of all the results ? | "answer sum of 100 result = sum of 60 result + sum of 40 result . = 60 x 40 + 40 x 60 = 4800 / 100 correct option : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"81 : 121",
"4 : 9",
"729 : 1331",
"27 : 121"
]
} | [
"B"
] | the ratio of the volumes of two cubes is 1000 : 3375 . what is the ratio of their total surface areas ? | "ratio of the sides = â ³ â ˆ š 1000 : â ³ â ˆ š 3375 = 10 : 15 ratio of surface areas = 10 ^ 2 : 15 ^ 2 = 100 : 225 = 4 : 9 answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 8908.42",
"rs . 9720",
"rs . 10123.20",
"rs . 10483.20"
]
} | [
"A"
] | what will be the compound interest on a sum of rs . 22,000 after 3 years at the rate of 12 % p . a . ? | "amount = [ 22000 * ( 1 + 12 / 100 ) 3 ] = 22000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 30908.42 c . i . = ( 30908.42 - 22000 ) = rs . 8908.42 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"69",
"72",
"75",
"71"
]
} | [
"D"
] | the average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew , who weighs 53 kg is replaced by a new man . find the weight of the new man . | "total weight increased = ( 1.8 x 10 ) kg = 18 kg . : . weight of the new man = ( 53 + 18 ) kg = 71 kg . answer is d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7500",
"8880",
"6200",
"5200"
]
} | [
"B"
] | 80 x 100 + 80 x 11 = ? | "= 80 x ( 100 + 11 ) ( by distributive law ) = 80 x 111 = 8880 answer is b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4 / 19",
"7 / 19",
"12 / 37",
"21 / 95"
]
} | [
"C"
] | a box contains 23 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is | solution p ( none is defective ) = 19 c 2 / 23 c 2 = 25 / 37 . p ( at least one is defective ) = ( 1 - 25 / 37 ) = 12 / 37 . answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2,000', '",
"1,800', '",
"1,900', '",
"1,700', '"
]
} | [
"C"
] | a rectangular lawn 70 m × 30 m has two roads each 5 metres wide , running in the middle of it , one parallel to the length and the other parallel to the breadth . find the cost of gravelling the road at the rate of 4 per square metre . | total area of road = area of road which parallel to length + area of road which parallel to breadth – overlapped road = 70 × 5 + 30 × 5 – 5 × 5 = 350 + 150 – 25 = 500 – 25 = 475 m 2 ∴ cost of gravelling the road = 475 × 4 = 1900 answer c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 : 3",
"4 : 3",
"3 : 6",
"4 : 5"
]
} | [
"A"
] | two cars , one from austin to dallas and the other from dallas to austin , start simultaneously . after they meet , the cars reach their destinations after 4 hours and 9 hours respectively the ratio of their speeds is | solution let us name the cars as a and b . = ( car a ' s speed ) : ( car b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 4 : â ˆ š 9 = 2 : 3 answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20 * ( sqr 2 - 1 )', '",
"8 * ( sqr 3 - 1 )', '",
"4 * ( sqr 7 - 1 )', '",
"12 * ( sqr 7 - 1 )', '"
]
} | [
"A"
] | consider a quarter of a circle of radius 20 . let r be the radius of the circle inscribed in this quarter of a circle . find r . | i got 20 / ( sqr 2 + 1 ) and just forgot to multiply by ( sqr 2 - 1 ) . answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"95",
"99",
"26",
"73"
]
} | [
"B"
] | what two - digit number is less than the sum of the square of its digits by 12 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 - 12 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 12 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 . . . thus the two numbers can be 15 or 99 thus the answer is b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"13000",
"7000",
"10000",
"5000"
]
} | [
"D"
] | a textile manufacturing firm employees 70 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 70 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is : | explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 69 / 70 ) â ˆ ’ 150000 ã — ( 69 / 70 ) â ˆ ’ 75000 . = > rs 2 , 70,000 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 70,000 = > rs . 5,000 . answer : d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 12250",
"rs . 13375",
"rs . 16750",
"rs . 15000"
]
} | [
"D"
] | a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 55000 . what is the share of c ? | explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 55000 ] = rs . 15000 answer : option d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"588",
"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 1400 employees , then the no . of female employees who are computer literate ? | "solution : total employees , = 1400 female employees , 60 % of 1400 . = ( 60 * 1400 ) / 100 = 840 . then male employees , = 560 50 % of male are computer literate , = 280 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1400 ) / 100 = 868 computer literate . thus , female computer literate = 868 - 280 = 588 . answer : option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2574",
"2500",
"1485",
"1574"
]
} | [
"C"
] | if the product of two numbers is 17820 and their h . c . f . is 12 , find their l . c . m . | "explanation : hcf * lcm = 17820 , because we know product of two numbers = product of hcf and lcm lcm = 17820 / 12 = 1485 option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"E"
],
"text": [
"400",
"510",
"500",
"506"
]
} | [
"A"
] | evaluate 100 / . 25 | explanation : 100 / . 25 = 10000 / 25 = 400 option a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"5 kg",
"12,5 kg",
"25 kg",
"30 kg"
]
} | [
"B"
] | the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 10 kg of rice previously ? | "solution : let rs . 100 be spend on rice initially for 10 kg . as the price falls by 20 % , new price for 10 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 10 = rs . 8 per kg . rice can bought now at = 100 / 8 = 12,5 kg . answer : option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"22 hours",
"30 hours",
"44 hours",
"60 hours"
]
} | [
"C"
] | 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 r 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 ) ? | "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 job r in 44 hours . answer : c ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"720578",
"80578",
"80698",
"81268"
]
} | [
"A"
] | 617 x 617 + 583 x 583 = ? | "= ( 617 ) ^ 2 + ( 583 ) ^ 2 = ( 600 + 17 ) ^ 2 + ( 600 - 17 ) ^ 2 = 2 [ ( 600 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 360000 + 289 ] = 2 x 360289 = 720578 answer is a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 500",
"rs . 840",
"rs . 650",
"rs . 720"
]
} | [
"B"
] | a man invested rs . 14400 in rs . 100 shares of a company at 20 % premium . if the company declares 7 % dividend at the end of the year , then how much does he get ? | solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 7 / 100 x 12000 ) = rs . 840 . answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4.37 %",
"4 %",
"2.3 %",
"3.75 %"
]
} | [
"C"
] | the population of a town increased from 1 , 24,300 to 1 , 62,400 in a decade . the average percent increase of population per year is : | "explanation : increase in 10 years = ( 162400 - 124300 ) = 87500 . increase % = ( 38100 / 162400 x 100 ) % = 23 % . required average = ( 23 / 10 ) % = 2.3 % . answer : option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"51 : 52",
"52 : 53",
"53 : 54",
"54 : 55"
]
} | [
"B"
] | the cash difference between the selling prices of an article at a profit of 4 % and 6 % is rs 3 . the ratio of two selling prices is | "explanation : let the cost price of article is rs . x required ratio = 104 % of x / 106 % of x = 104 / 106 = 52 / 53 = 52 : 53 option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"5.12",
"4.13",
"6.15",
"7.5"
]
} | [
"A"
] | excluding stoppages , the speed of a bus is 82 kmph and including stoppages , it is 75 kmph . for how many minutes does the bus stop per hour ? | "due to stoppages , it covers 7 km less . time taken to cover 7 km = ( ( 7 / 82 ) ã — 60 ) = 5.12 min . option ( a ) is correct" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"6178.85",
"8032.5",
"4462.5",
"8900"
]
} | [
"A"
] | a sum fetched total simple interest of 4016.25 at the rate of 13 p . c . p . a . in 5 years . what is the sum ? | "let the sums be p . now , 65 % of p = 4016.25 or , p = 6178.85 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 / 6",
"4 / 120",
"29 / 30",
"1 / 9"
]
} | [
"C"
] | a classroom has 3 electric lamps . from a collocation of 10 electric bulbs of which 6 are good , 3 are selected at random and put in the lamps . find the probability that the room is lighted . | explanation : out of 10 electric bulbs , 3 are selected in 10 c 3 ways . so , number of possible outcomes = t = 10 c 3 = 120 . the room is lighted i . e at least one fo the 3 bulbs chosen at random is a good bulb . wherever ' at least one ' is present , it is easier to do the problem using complement of the event ( i . e room is dark and all 3 bulbs are bad ) . p ( room is dark ) = f / t = p ( none of the bulbs is good ) = > 4 c 3 / 120 . [ since 4 bulbs are bad ] . p ( room is lighted ) = 1 - ( 4 c 3 / 120 ) . [ room is lighted if at least one bulb is good ] . or p ( at least one ) = 1 - ( 4 / 120 ) . = 29 / 30 . answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7.2 kg .",
"10.8 kg .",
"12.4 kg .",
"6.1 kg"
]
} | [
"D"
] | if the weight of 12 meters long rod is 12.2 kg . what is the weight of 6 meters long rod ? | "answer ∵ weight of 12 m long rod = 12.2 kg ∴ weight of 1 m long rod = 12.2 / 12 kg ∴ weight of 6 m long rod = 12.2 x 6 / 12 = 6.1 kg option : d" | MathQA |
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