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": [
"600 m 2', '",
"540 m 2', '",
"680 m 2', '",
"574 m 2', '"
]
} | [
"A"
] | in a parallelogram , the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 metres respectively . find its area | in a parallelogram . area = diagonal Γ length of perpendicular on it . = 30 Γ 20 = 600 m 2 answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"750",
"700",
"800",
"850"
]
} | [
"C"
] | in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 320 vote β 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 % - - - - - > 320 ( 40 * 8 = 320 ) 100 % - - - - - > 800 ( 100 * 8 = 800 ) answer : option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"380",
"350",
"332",
"310"
]
} | [
"C"
] | ( 3136 + 6160 ) / 28 | "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9296 ) / 28 = 332 option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 / 20",
"3 / 20",
"4 / 20",
"5 / 20"
]
} | [
"B"
] | if you spend 1 / 4 of your salary during the first week of the month and 20 % of it during each of the coming 3 weeks , what part ( fraction ) of your salary will leave unspent at the end of the month ? | solution : 1 / 4 + 3 ( 20 / 100 ) = 1 / 4 + 3 / 5 = 5 + 12 / 20 = 17 / 20 the sallary that will be spent = 17 / 20 unspend will be = 1 β 17 / 20 = 20 β 17 / 20 = 3 / 20 answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4500",
"7500",
"5000",
"6000"
]
} | [
"D"
] | the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 15 . find the sum : | "sol . ( d ) let the sum be 100 . therefore , si = 100 Γ 5 Γ 2100 = 10100 Γ 5 Γ 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 β 100100 ( 1 + 5100 ) 2 β 100 β΄ = 100 Γ 21 Γ 2120 Γ 20 β 100 = 414 = 100 Γ 21 Γ 2120 Γ 20 β 100 = 414 difference of ci and si = 41 β 4 - 10 = 1 β 4 if the difference is 1 β 4 , the sum = 100 = > if the difference is 15 , the sum = 400 Γ 15 = 6000 answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"380",
"350",
"331",
"310"
]
} | [
"C"
] | ( 3108 + 6160 ) / 28 | "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9268 ) / 28 = 331 option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 hours",
"12 hours",
"14 hours",
"24 hours"
]
} | [
"D"
] | in a river flowing at 2 km / hr , a boat travels 64 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time . | "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 64 km total time taken = time taken downstream + time taken upstream = ( 64 / 8 ) + ( 64 / 4 ) = = 24 hr . answer : option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7",
"16",
"10",
"11"
]
} | [
"A"
] | define a = the sum of digits of the number 7 ^ 100 and b = the sum of the digits of a . what is the sum of the digits of b ? | following approach will take you only couple of sec . \ ( 7 ^ { 100 } = ( 7 ^ { 50 } ) ^ 2 \ ) the sum of digits ( digital root ) of a perfect square can only be 1 , 4 , 7 or 9 . for example \ ( 7 ^ 2 = 49 \ ) = > dr = 4 + 9 = 13 = > 1 + 3 = 4 and etc . checking available options . answer a . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"24",
"17",
"28",
"42"
]
} | [
"D"
] | two sets of 7 consecutive positive integers have exactly one integer in common . the sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set ? | a = ( 1 , 2,3 , 4,5 , 6,7 ) , sum of this = 28 b = ( 7 , 8,9 , 10,11 , 12,13 ) , sum of this = 70 the differenct between 70 - 28 = 42 hence , 42 is the answer i . e . d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"12541', '",
"12542', '",
"12544', '",
"12545', '"
]
} | [
"C"
] | a lady grows cauliflower in her garden that is in the shape of a square . each cauliflower takes 1 square foot of area in her garden . this year , she has increased her output by 223 cauliflower when compared to last year . the shape of the area used for growing the cauliflower has remained a square in both these years . how many cauliflowers did she produce this year ? | explanatory answer the shape of the area used for growing cauliflower has remained a square in both the years . let the side of the square area used for growing cauliflower this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing cauliflower last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of cauliflower grown has increased by 223 , the area would have increased by 223 sq ft because each cauliflower takes 1 sq ft space . hence , x 2 - y 2 = 223 ( x + y ) ( x - y ) = 223 . 223 is a prime number and hence it will have only two factors . i . e . , 223 and 1 . therefore , 223 can be expressed as product of 2 numbers in only way = 223 * 1 i . e . , ( x + y ) ( x - y ) = 223 * 1 so , ( x + y ) should be 223 and ( x - y ) should be 1 . solving the two equations we get x = 112 and y = 111 . therefore , number of cauliflower produced this year = x 2 = 1122 = 12544 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice a , b and d . as 12541,12542 and 12545 are not the square of any number . check choice c : if this year ' s produce is 12544 , last year ' s produce would have been 12544 - 223 = 12321 12321 is the square of 111 . so , 12544 is the answer . choice c . | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 hours",
"3 hours",
"4 hours",
"5 hours"
]
} | [
"C"
] | a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 4 km / hr . find the time taken by the boat to go 68 km downstream ? | "solution speed downstream = ( 13 + 4 ) km / hr = 17 km / hr . time taken to travel 68 km downstream = ( 68 / 17 ) hrs = 4 hrs . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"130",
"620",
"147",
"120"
]
} | [
"C"
] | what is the compound interest paid on a sum of rs . 700 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 % 700 = 700 * ( 21 / 100 ) = 147 answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"11 , 12,13",
"15 , 11,13",
"15 , 11.25 , 18.75",
"11 , 15.25 , 18.75"
]
} | [
"C"
] | a can do piece of work in 15 days and b in 20 days they finished the work with the assistance of c in 5 days and got rs . 45 as their wages find the share for each in wages ? | explanation : a β s 1 day work = 1 / 3 b β s 1 day work = 1 / 4 c β s 1 day work = 1 - 1 / 4 - 1 / 3 = 5 / 12 a β s share = 45 * 1 / 3 = 15 b β s share = 45 * 1 / 4 = 11.25 c β s share = 45 * 5 / 12 = 18.75 answer : option c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"β 220",
"β 100",
"100",
"135"
]
} | [
"C"
] | if the average ( arithmetic mean ) of a and b is 210 , and the average of b and c is 160 , what is the value of a β c ? | "question : a - c = ? ( a + b ) / 2 = 210 = = = > a + b = 420 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 420 - 320 = = = > a + b - b - c = 100 = = = > a - c = 100 answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"6",
"36",
"19",
"27"
]
} | [
"B"
] | 765 chairs are to be arranged in a column in such a way that the number of chairs in each column should be equal to the columns . how many chairs will be excluded to make this arrangement possible ? | 27 ( 2 ) < 765 < 28 ( 2 ) β΄ required no . of chairs to be excluded = 765 β 729 = 36 answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1010",
"804",
"814",
"844"
]
} | [
"A"
] | what is the least number of square tiles required to pave the floor of a room 12 m 12 cm long and 1 m 20 cm broad ? | "solution length of largest tile = h . c . f . of 1212 cm & 120 cm = 12 cm . area of each tile = ( 12 x 12 ) cm 2 β΄ required number of tiles = [ 1212 x 120 / 12 x 12 ] = 1010 . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3 / 5",
"5 / 3",
"15",
"25"
]
} | [
"B"
] | if 2 x = 3 β 32 , then x is equal to : | "sol . 2 x = 3 β 32 β 2 x = ( 32 ) 1 / 3 = ( 25 ) 1 / 3 = 25 / 3 β x = 5 / 3 . answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"40",
"54",
"45",
"50"
]
} | [
"D"
] | a worker makes a toy in every 3 h . if he works for 150 h , then how many toys will he make ? | no . of toys = 150 / 3 = 50 answer : d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 1950",
"rs 2000",
"rs 745",
"rs 765"
]
} | [
"A"
] | if an amount of rs 42,900 is distributed equally amongst 22 persons , how much amount would each person get ? | required amount = 42900 / 22 = rs 1950 answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10 hours",
"12 hours",
"14 hours",
"18 hours"
]
} | [
"D"
] | in a river flowing at 2 km / hr , a boat travels 48 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time . | "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance traveled downstream = distance traveled upstream = 48 km total time taken = time taken downstream + time taken upstream = ( 48 / 8 ) + ( 48 / 4 ) = 18 hr . answer : option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"630",
"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 1500 employees , then the no . of female employees who are computer literate ? | "solution : total employees , = 1500 female employees , 60 % of 1500 . = ( 60 * 1500 ) / 100 = 900 . then male employees , = 600 50 % of male are computer literate , = 300 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1500 ) / 100 = 930 computer literate . thus , female computer literate = 930 - 300 = 630 answer : option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 21.81",
"rs . 12",
"rs . 12.25",
"rs . 12.31"
]
} | [
"A"
] | a fruit seller sells mangoes at the rate of rs . 16 per kg and thereby loses 12 % . at what price per kg , he should have sold them to make a profit of 20 % ? | "solution 88 : 16 = 120 : x x = ( 16 Γ£ β 120 / 88 ) = rs . 21.81 hence , s . p per kg = rs . 21.81 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"400",
"525",
"750",
"850"
]
} | [
"C"
] | the length of a train and that of a platform are equal . if with a speed of 90 k / hr , the train crosses the platform in one minute , then the length of the train ( in metres ) is : | "sol . speed = [ 90 * 5 / 18 ] m / sec = 25 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x metres . then , 2 x / 60 = 25 β x = 25 * 60 / 2 = 750 answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 9000.30",
"rs . 9720",
"rs . 10123.20",
"rs . 10483.20"
]
} | [
"C"
] | what will be the compound interest on a sum of rs . 25,000 after 3 years at the rate of 12 p . c . p . a . ? | "explanation : amount = rs . [ 25000 x ( 1 + 12 / 100 ) 3 ] = rs . 35123.20 c . i . = rs . ( 35123.20 - 25000 ) = rs . 10123.20 answer is c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"100",
"160",
"120",
"200"
]
} | [
"D"
] | 4 - fifths of 3 - eighths of a number is 24 . what is 250 per cent of that number ? | let the number = x . 4 β 5 Γ 3 β 8 x = 24 or x = 24 Γ 2 Γ 5 / 3 = 80 β΄ 250 per cent of the number = 250 β 100 Γ 80 = 200 answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"8163",
"8633",
"8663",
"8636"
]
} | [
"B"
] | find the mean proportional between 7921 & 9409 ? | "explanation : formula = β a Γ b a = 7921 and b = 9409 β 7921 Γ 9409 = 89 Γ 97 = 8633 answer : option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"10.8",
"18",
"25",
"30"
]
} | [
"D"
] | a train moves with a speed of 108 kmph . its speed in metres per second is | "sol . 108 kmph = [ 108 x 5 / 18 ] m / sec = 30 m / sec . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"75",
"81",
"71",
"79"
]
} | [
"D"
] | a , b , c , d and e are ve consecutive odd numbers the sum of a and c is 146 . what is the value of e ? | a + c = 146 β a + a + 4 = 146 β a = 146 - 4 / 2 = 71 β΄ e = a + 8 = 71 + 8 = 79 answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4.58 %",
"5.96 %",
"6.52 %",
"4.98 %"
]
} | [
"B"
] | at what rate percent on simple interest will rs . 415 amount to rs . 514 in 4 years ? | "explanation : difference in amount = 514 - 415 = 99 99 = ( 415 x 4 x r ) / 100 r = 5.96 % answer is b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1.6 km",
"2 km",
"6.3 km",
"4 km"
]
} | [
"C"
] | the speed of a boat in still water is 21 km / hr and the rate of current is 8 km / hr . the distance travelled downstream in 13 minutes is | "explanation : speed downstreams = ( 21 + 8 ) kmph = 18 kmph . distance travelled = ( 29 x 13 / 60 ) km = 6.3 km option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"34",
"40",
"85",
"88"
]
} | [
"C"
] | a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 650 sq . feet , how many feet of fencing will be required ? | "explanation we have : l = 20 ft and lb = 650 sq . ft . so , b = 32.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 65 ) ft = 85 ft . answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"21.2 kmph",
"12.1 kmph",
"23.4 kmph",
"20.4 kmph"
]
} | [
"A"
] | mike took a bus from home to market , that travels at 30 kmph . while walking back at 6 kmph , halfway through , he suddenly realized he was getting late and he cycled back the remaining distance in 20 kmph . find the average speed . | let the distance be 2 x ( one way ) time taken by bus = 2 x / 30 , by walking = x / 6 , by cycling = x / 20 hours : . average speed = total distance / total time = 6 x / x / 15 + x / 6 + x / 20 = 6 * 60 / 4 + 10 + 3 = 21.2 answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"26",
"27",
"46",
"57"
]
} | [
"B"
] | the sum of 3 consecutive multiples of 3 is 72 . what is the larget number ? | sol . let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 72 β 9 x = 63 β x = 7 . β΄ largest number = 3 x + 6 = 27 . answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"30 %",
"53 %",
"90 %",
"100 %"
]
} | [
"B"
] | in a restaurant , the profit is 140 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ? | "explanation : let c . p . = rs . 100 . then , profit = rs . 140 , s . p . = rs . 240 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 240 . profit = rs . ( 240 - 112 ) = rs . 128 . required percentage = ( 128 / 240 * 100 ) % = 53 % appox answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"120",
"160",
"132",
"130"
]
} | [
"A"
] | in an office , totally there are 800 employees and 25 % of the total employees are males . 40 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ? | "number of male employees = 800 * 25 / 100 = 200 required number of male employees who are less than 50 years old = 200 * ( 100 - 40 ) % = 200 * 60 / 100 = 120 . answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"8925",
"8032.5",
"4462.5",
"8900"
]
} | [
"B"
] | a sum fetched total simple interest of 4016.25 at the rate of 10 p . c . p . a . in 5 years . what is the sum ? | let the sums be p . now , 50 % of p = 4016.25 or , p = 8032.5 answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.68",
"0.6",
"0.8",
"0.3"
]
} | [
"D"
] | ( 1.2 ) ( power 3 ) - ( 0.9 ) ( power 3 ) / ( 1.2 ) ( power 2 ) + 1.08 + ( 0.9 ) ( power 2 ) is : | "given expression = ( 1.2 ) ( power 3 ) - ( 0.9 ) ( power 3 ) / ( 1.2 ) ( power 2 ) + ( 1.2 x 0.9 ) + ( 0.9 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 1.2 - 0.9 ) = 0.3 answer is d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"50",
"30",
"125",
"25"
]
} | [
"B"
] | if the l . c . m of two numbers is 600 and their product is 18000 , find the h . c . f of the numbers . | "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 18000 / 600 = 30 . answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"9 , 10",
"10 , 11",
"11 , 12",
"12 , 13"
]
} | [
"A"
] | the sum of the squares of two consecutive positive integers exceeds their product by 91 . find the integers ? | let the two consecutive positive integers be x and x + 1 x 2 + ( x + 1 ) 2 - x ( x + 1 ) = 91 x 2 + x - 90 = 0 ( x + 10 ) ( x - 9 ) = 0 = > x = - 10 or 9 . as x is positive x = 9 hence the two consecutive positive integers are 9 and 10 . answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 600",
"rs . 618",
"rs . 525",
"rs . 620"
]
} | [
"B"
] | find compound interest on rs . 5000 at 12 % per annum for 1 year , compounded half - yearly . | "principal = rs . 5000 , rate = 6 % per half year time = 1 year = 2 half - years amount = rs . { 5000 x ( 1 + 6 / 100 ) 2 ] = rs . [ 5000 x 53 / 50 x 53 / 50 ] = rs . 5618 c . i . = rs . ( 5618 β 5000 ) = rs . 618 answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1 / 16",
"1 / 19",
"1 / 4",
"1 / 3"
]
} | [
"B"
] | a consignment of 20 picture tubes contains 5 defectives . two tubes are selected one after the other at random . the probability that both are defective assuming that the first tube is not replaced before drawing the second , would be : | probability of drawing a defective tube in first draw is 5 / 20 probability of drawing a defective tube in second draw ( without replacing first tube ) is 4 / 19 . therefore probability of getting both defective is = ( 5 / 20 ) * ( 4 / 19 ) = 1 / 19 answer : b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 40000",
"rs . 36000",
"rs . 50000",
"rs . 25000"
]
} | [
"D"
] | raja spends 60 % of his monthly income on household items , 10 % of his monthly income on buying cloths , 10 % of his monthly income on medicines and saves the remaining amount which is rs . 5000 . find his monthly income . | "savings 20 % - 5000 expenditure 80 % - 20000 total - 25000 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.22085",
"2.2085",
"0.022085",
"0.0022085"
]
} | [
"C"
] | 22.085 Γ£ β 0.001 = ? | "22.085 Γ£ β 0.001 = ? or , ? = 0.022085 answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"82 m",
"50 m",
"72 m",
"150 m"
]
} | [
"D"
] | two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 108 seconds . the length of each train is : | "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 Γ 518 = 259 m / s in 108 secs the total distance traveled is 108 x 25 / 9 = 300 m . therefore the length of each train is = 300 / 2 = 150 m . answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4038",
"8076",
"9691.2",
"4845.6"
]
} | [
"A"
] | mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 48456 , how much amount per month would he have spent on clothes and transport ? | β΅ amount , he have spent in 1 month on clothes transport = amount spent on saving per month β΅ amount , spent on clothes and transport = 48456 β 12 = 4038 answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 147.50",
"rs . 785.50",
"rs . 176.50",
"rs . 258.50"
]
} | [
"C"
] | teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 154 per kg , the price of the third variety per kg will be ? | "explanation : since first and 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 . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 154 ) / \ x Γ’ Λ β 154 22.50 = > x Γ’ Λ β ( 154 / 22.50 ) = 1 . = > x Γ’ Λ β 154 = 22.50 . = > x = 176.50 rs . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 27,000",
"rs . 24,000",
"rs . 30,000",
"rs . 36,000"
]
} | [
"A"
] | jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 54,000 after completion of one year . what will be madhu ' s share of profit ? | "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 54,000 i . e . rs . 27,000 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"70 %",
"60 %",
"30 %",
"75 %"
]
} | [
"B"
] | the ratio 15 : 25 expressed as percent equals to | "explanation : actually it means 15 is what percent of 25 , which can be calculated as , ( 15 / 25 ) * 100 = 15 * 4 = 60 answer : option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3 : 1",
"3 : 2",
"3 : 5",
"4 : 1"
]
} | [
"D"
] | if the volume of two cubes are in the ratio 64 : 1 , the ratio of their edges is : | "explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 64 / 1 = > ( a / b ) 3 = ( 4 / 1 ) 3 a / b = 4 / 1 = > a : b = 4 : 1 option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.1503",
"0.001503",
"1.503",
"0.001503"
]
} | [
"A"
] | 15.03 Γ£ β 0.01 = ? | "15.03 Γ£ β 0.01 = ? or , ? = 0.1503 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"3025",
"4200",
"3060",
"3210"
]
} | [
"A"
] | { ( 481 + 426 ) 2 - 4 x 481 x 426 } = ? | "explanation : here , the given statement is like ( a + b ) 2 - 4 ab where a = 481 and b = 426 ( a + b ) 2 - 4 ab = ( a 2 + 2 ab + b 2 ) - 4 ab = a 2 - 2 ab + b 2 = ( a - b ) 2 hence { ( 481 + 426 ) 2 - 4 x 481 x 426 } = ( 481 - 426 ) 2 = 552 = 3025 . answer : option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"960",
"1060",
"1,200",
"945"
]
} | [
"D"
] | the profit earned by selling an article for 812 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ? | "let the profit or loss be x and 812 β x = 448 + x or , x = 364 β 2 = 182 \ cost price of the article = 812 β x = 448 + x = 630 \ sp of the article = 630 Γ 150 β 100 = 945 answer d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"150",
"160",
"140",
"130"
]
} | [
"D"
] | what is the angle between the minute hand and the hour hand when the time is 1540 hours ? | solution : the total angle made by the minute hand during an hour is 360 o . if it takes 360 o for an hour , it will take ( 40 / 60 ) * 360 = 240 o . the angle between the hour hand the minute hand will therefore , be somewhere between 240 - 90 = 150 o , as the hour hand is between 3 and 4 . the angle made by the hour hand when it moves from say 3 to 4 will be 30 o . that is the hour hand makes 30 o during the course of an hour . the hour hand will therefore , move ( 40 / 60 ) * 30 = 20 o . therefore , the net angle between the hour hand and the minute hand will be 150 - 20 = 130 o . answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0",
"1",
"27",
"0"
]
} | [
"D"
] | for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.567 ] = 1 and [ 1.999 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ? | k = [ lcm of 80 and 45 ] * ( any integer ) however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer for value of k ( 60 ) * any integer unit value will be always zero . d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"52 kmph .",
"62 kmph .",
"72 kmph .",
"80 kmph ."
]
} | [
"A"
] | a man sitting in a train which is travelling at 60 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ? | "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 60 ) kmph = 52 kmph . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 420000",
"rs . 180000",
"rs . 436800",
"rs . 504000"
]
} | [
"C"
] | the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 13000 , then find the annual income of a ? | "b ' s monthly income = 13000 * 112 / 100 = rs . 14560 b ' s monthly income = 2 parts - - - - > rs . 14560 a ' s monthly income = 5 parts = 5 / 2 * 14560 = rs . 36400 a ' s annual income = rs . 36400 * 12 = rs . 436800 answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 49.17",
"rs . 51.03",
"rs . 54.17",
"rs . 55.66"
]
} | [
"D"
] | if 10 litres of an oil of rs . 50 per litres be mixed with 5 litres of another oil of rs . 67 per litre then what is the rate of mixed oil per litre ? | "50 * 10 = 500 67 * 5 = 335 835 / 15 = 55.66 answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 950",
"rs . 1500",
"rs . 1000",
"rs . 2200"
]
} | [
"D"
] | a trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 55 per metre of cloth . how much profit will the trder earn on 40 metres of cloth ? | explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 β 55 = rs . 150 cp on 40 metres = 150 x 40 = rs . 6000 profit earned on 40 metres cloth = rs . 8200 β rs . 6000 = rs . 2200 . answer : option d | MathQA |
{
"label": [
"A",
"B",
"C",
"E"
],
"text": [
"13",
"12 , 45",
"1 , 25",
"12 , 35"
]
} | [
"E"
] | if a and b are multiples of 3 then which are all the multiples of 3 1 ) a / b 2 ) a ^ b 3 ) a + b 4 ) a - b 5 ) a * b | a * b a ^ b a + b a - b are multiples of 3 except a / b answer : e | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"51 : 52",
"52 : 53",
"53 : 54",
"54 : 55"
]
} | [
"C"
] | the cash difference between the selling prices of an article at a profit of 6 % and 8 % is rs 3 . the ratio of two selling prices is | "explanation : let the cost price of article is rs . x required ratio = ( 106 % of x ) / ( 108 % of x ) = 106 / 108 = 53 / 54 = 53 : 54 . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"16",
"24",
"20",
"32"
]
} | [
"A"
] | if 20 % of 30 is greater than 25 % of a number by 2 , the number is : | explanation : = > 20 / 100 * 30 - 25 / 100 * x = 2 = > x / 4 = 4 so x = 16 answer : a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"6630",
"6650",
"6560",
"6530"
]
} | [
"A"
] | 15 51 216 1100 ? 46452 | "the format of the series 15 * 3 + 6 = 51 51 * 4 + 12 = 216 216 * 5 + 20 = 1100 1100 * 6 + 30 = 6630 6630 * 7 + 42 = 46452 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"315",
"345",
"325",
"375"
]
} | [
"D"
] | what annual installment will discharge a debt of rs . 1260 due in 3 years at 12 % simple interest ? | "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1260 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1260 Γ― Ζ βΊ ( 28 x + 31 x + 25 x ) = ( 1260 * 25 ) x = ( 1260 * 25 ) / 84 = rs . 375 . therefore , each installment = rs . 375 . answer is d ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"300",
"400",
"562.5",
"600"
]
} | [
"C"
] | there are 225 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 ) + 225 ( 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 + 225 = 2 / 5 t , or 2 / 5 ( t - m ) = 225 , from here we get that t - m = 562.5 , that would be total number of female employees and the answer ( c ) | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"22.8 kg",
"25.6 kg",
"28 kg",
"26.5 kg"
]
} | [
"A"
] | if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 6 m of the same rod ? | "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 6 : : 42.75 : x = > 11.25 x x = 6 x 42.75 = > x = ( 6 x 42.75 ) / 11.25 = > x = 22.8 answer : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"124 m 2', '",
"120 m 2', '",
"108 m 2', '",
"58 m 2', '"
]
} | [
"A"
] | the floor of a rectangular room is 15 m long and 12 m wide . the room is surrounded by a verandah of width 2 m on all its sides . the area of the verandah is : | area of the outer rectangle = 19 Γ 16 = 304 m 2 area of the inner rectangle = 15 Γ 12 = 180 m 2 required area = ( 304 β 180 ) = 124 m 2 answer a | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1100",
"800",
"1400",
"1200"
]
} | [
"D"
] | a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 6600 . what is the share of b ? | "let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a β s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 6600 x ( 2 / 11 ) ) = rs . 1200 . answer is d ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.1",
"0.4",
"0.82",
"0.8"
]
} | [
"B"
] | if 0.60 : x : : 6 : 4 , then x is equal to | "sol . ( x Γ 6 ) = ( 0.60 Γ 4 ) β x = 2.4 / 6 = 0.40 . answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2436",
"2801",
"- 1496",
"- 2071"
]
} | [
"C"
] | - 84 x 19 + 100 = ? | "given exp . = - 84 x ( 20 - 1 ) + 100 = - ( 84 x 20 ) + 84 + 100 = - 1680 + 184 = - 1496 answer is c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20 m",
"25 m",
"22.5 m",
"9 m"
]
} | [
"A"
] | in a 100 m race , a covers the distance in 36 seconds and b in 45 second . in this race a beats b by : | "solution distance covered by b in 9 sec . = ( 100 / 45 x 9 ) m = 20 m . β΄ a beats b by 20 metres . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"7 m",
"7.5 m",
"8 m",
"8.5 m"
]
} | [
"B"
] | the cost of carpeting a room 18 m long with a carpet 75 cm wide at 4.50 per metre is 810 . the breadth of the room is : | length of the carpet = totalcost / rate / m = ( 8100 β 45 ) m = 180 m . area of the room = area of the carpet = ( 180 Γ 75 β 100 ) m 2 = 135 m 2 β΄ breadth of the room = arealength = 135 / 18 m = 7.5 m answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 19",
"rs . 22",
"rs . 20",
"rs . 21"
]
} | [
"D"
] | the present worth of a certain bill due sometime hence is rs . 400 and the true discount is rs . 20 . what is the banker ' s discount ? | "explanation : bg = ( td ) 2 / pw = 202 / 400 = rs . 1 bg = bd β td = > 1 = bd - 20 = > bd = 1 + 20 = rs . 21 answer : option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 432",
"rs . 422",
"rs . 416",
"rs . 442"
]
} | [
"C"
] | the true discount on a bill of rs . 2660 is rs . 360 . what is the banker ' s discount ? | "explanation : f = rs . 2660 td = rs . 360 pw = f - td = 2660 - 360 = rs . 2300 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2300 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2160 for unexpired time = 360 / 2300 Γ 2660 = 0.16 Γ 2660 = rs . 416 answer : option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"18",
"8",
"12",
"10"
]
} | [
"D"
] | find the greatest number which leaves the same remainder when it divides 20 , 40 and 90 . | "90 - 40 = 50 40 - 20 = 20 90 - 20 = 70 the h . c . f of 20 , 50 and 70 is 10 . answer : d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"110 hours",
"112 hours",
"115 hours",
"100 hours"
]
} | [
"B"
] | two pipes can fill a cistern in 14 and 16 hours respectively . the pipes are opened simultaneously and it is found that due to leakage in the bottom , 32 minutes extra are taken for the cistern to be filled up . if the cistern is full , in what time would the leak empty it ? | cistern filled by both pipes in one hour = 1 β 14 + 1 β 16 = 15 β 112 th β΄ both pipes filled the cistern in 112 β 15 hrs . now , due to leakage both pipes filled the cistern in 112 β 15 + 32 β 60 = 8 hrs . β΄ due to leakage , filled part in one hour 1 β 8 β΄ part of cistern emptied , due to leakage in one hour = 15 β 112 - 1 β 8 = 1 β 112 th β΄ in 112 hr , the leakage would empty the cistern . answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"100",
"250",
"300",
"330"
]
} | [
"A"
] | the radius of the wheel of a bus is 175 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 = 175 cm . then , circumference of wheel = 2 Γ― β¬ r = 350 Γ― β¬ = 1100 cm distance covered by bus in 1 minute = 66 Γ’ Β β 60 Γ£ β 1000 Γ£ β 100 cms distance covered by one revolution of wheel = circumference of wheel = 1100 cm Γ’ Λ Β΄ revolutions per minute = 6600000 / 60 Γ£ β 1100 = 100 answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2 hr 30 min",
"2 hr",
"4 hr",
"1 hr 15 min"
]
} | [
"A"
] | a boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes . how long will it take to go 5 km in stationary water ? | "explanation : speed upstream = 2 / 2 = 1 km / hr speed downstream = 1 / ( ( 20 / 60 ) ) = 3 km / hr speed in still water = 1 / 2 ( 3 + 1 ) = 2 km / hr time taken to travel 5 km in still water = 5 / 2 = 2 ( 1 / 2 ) hours = 2 hour 30 minutes . answer : option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"0.7",
"0.07",
"0.007",
"7"
]
} | [
"B"
] | the cube root of . 000343 is | "explanation : ( . 000343 ) 1 / 3 = ( 343 / 106 ) 1 / 3 = ( 7 * 7 * 7 / 102 * 102 * 102 ) 1 / 3 = 7 / 102 = 7 / 100 = 0.07 answer b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"296",
"252",
"344",
"388"
]
} | [
"C"
] | the sum of 4 consecutive even numbers is 36 . find the sum of the squares of these numbers ? | let the four numbers be x , x + 2 , x + 4 and x + 6 . = > x + x + 2 + x + 4 + x + 6 = 36 = > 4 x + 12 = 36 = > x = 6 the numbers are 6 , 8 , 10 and 12 . sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344 . answer : c | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20 %",
"13.50 %",
"14 %",
"14.50 %"
]
} | [
"A"
] | an uneducated retailer marks all his goods at 60 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ? | "sol . let c . p . = rs . 100 . then , marked price = rs . 160 . s . p . = 75 % of rs . 160 = rs . 120 . β΄ gain % = 20 % . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 8.81",
"rs 9.81",
"rs 10.81",
"rs 11.81"
]
} | [
"D"
] | a fruit seller sells mangoes at the rate of rs . 9 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 % | "explanation : 85 : 9 = 105 : x x = ( 9 Γ 105 / 85 ) = rs 11.81 option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"20 %",
"15 %",
"33.33 %",
"18 %"
]
} | [
"B"
] | a milk man has 10 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is : | "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 10 liters of milk . therefore , profit percentage = 15 % . answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"β 220",
"β 200",
"100",
"135"
]
} | [
"B"
] | if the average ( arithmetic mean ) of a and b is 80 , and the average of b and c is 180 , what is the value of a β c ? | "a + b = 160 b + c = 360 a - c = - 200 . imo option b ." | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"500",
"600",
"700",
"800"
]
} | [
"C"
] | a sum was put at simple interest at a certain rate for 4 years had it been put at 2 % higher rate , it would have fetched 56 more . find the sum . | "difference in s . i . = p Γ t / 100 ( r 1 β r 2 ) β 56 = p Γ 4 Γ 2 / 100 ( β΅ r 1 - r 2 = 2 ) β p = 56 Γ 100 / 4 Γ 2 = 700 answer c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"64 %",
"65 %",
"66 %",
"67 %"
]
} | [
"A"
] | a student multiplied a number by 3 / 5 instead of 5 / 3 . what is the percentage error . | "explanation : let the number be x , then , 5 / 3 β 3 / 5 = 16 / 15 x error % = ( 16 / 15 x β 3 / 5 β 100 ) option a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"54",
"76",
"152",
"384"
]
} | [
"D"
] | the greatest number by which the product of 3 consecutive multiples of 4 is always divisible is | solution required number = product of first three multiplies of 3 = ( 4 Γ£ β 8 Γ£ β 12 ) = 384 . answer d | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"6",
"12",
"24",
"48"
]
} | [
"B"
] | if β 2 n = 64 , then the value of n is : | sol . β 2 n = 64 β ( 2 n ) 1 / 2 β 2 n / 2 = 26 β n / 2 = 6 β n = 12 . answer b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"28000",
"30000",
"31500",
"34000"
]
} | [
"C"
] | 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 4500 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 = 4500 = > total profit = 4500 * 7 = 31500 . answer : option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 147.50",
"rs . 785.50",
"rs . 177.50",
"rs . 258.50"
]
} | [
"C"
] | teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 155 per kg , the price of the third variety per kg will be ? | "explanation : since first and 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 . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 155 ) / \ x Γ’ Λ β 155 22.50 = > x Γ’ Λ β ( 155 / 22.50 ) = 1 . = > x Γ’ Λ β 155 = 22.50 . = > x = 177.50 rs . answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"130 km",
"120 km",
"100 km",
"140 km"
]
} | [
"C"
] | a bus covered a distance of 250 km , partly at an average speed of 40 kmph and partly at 60 kmph . if the total time taken is 5 hours , then the distance covered at 40 kmph is | "let the partial distance covered at 40 kmph be x let the another partial distance covered at 60 kmph be ( 250 - x ) thus , x / 40 - ( 250 - x ) / 60 = 5 or , x / 40 + ( 250 - x ) / 60 = 5 or , ( 3 x + 500 - 2 x ) / / 120 = 5 or 500 + x = 600 x = 100 answer : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"4",
"0",
"2",
"5"
]
} | [
"B"
] | what is the remainder when 8 ^ 1 + 8 ^ 2 + 8 ^ 3 + . . . + 8 ^ 9 is divided by 8 ? | "notice that in the brackets we have the sum of 9 even multiples of 8 , which yields remainder of 0 upon division by 8 . answer : b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 21724.14",
"rs . 31724.14",
"rs . 51724.14",
"rs . 61724.14"
]
} | [
"C"
] | a man sells a car to his friend at 13 % 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 Γ£ β 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 13 % . now s . p = rs . 45000 and loss = 13 % c . p . rs . [ 100 / 87 Γ£ β 45000 ] = rs . 51724.14 . correct option : c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"600",
"500",
"400",
"300"
]
} | [
"B"
] | a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are | explanation : given that the student got 125 marks and still he failed by 40 marks = > the minimum pass mark = 125 + 40 = 165 given that minimum pass mark = 33 % of the total mark = > total mark Γ ( 33 / 100 ) = 165 = > total mark = 16500 / 33 = 500 answer : option b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"25.5",
"2.5",
"12.5",
". 25"
]
} | [
"C"
] | 1 / 0.08 is equal to | "explanation : 1 / 0.08 = ( 1 * 100 ) / 8 = 100 / 8 = 12.5 option c" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs 600",
"rs 625",
"rs 650",
"rs 675"
]
} | [
"B"
] | the difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4 % per annum is rs 1 . find the sum | explanation : let the sum be p s . i . = p β 4 β 2 / 100 = 2 p / 25 c . i . = p ( 1 + 4 / 100 ) 2 β p = 676 p / 625 β p = 51 p / 625 as , c . i . - s . i = 1 = > 51 p / 625 β 2 p / 25 = 1 = > 51 p β 50 p / 625 = 1 p = 625 option b | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"rs . 70",
"rs . 36",
"rs . 54",
"rs . 50"
]
} | [
"A"
] | the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 8.4 . the true discount is | "solution t . d = [ b . g x 100 / r x t ] = rs . ( 8.4 x 100 / 12 x 1 ) = rs . 70 . answer a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"57600",
"44000",
"34936",
"25640"
]
} | [
"A"
] | 40 % of the population of a village is 23040 . the total population of the village is ? | "answer β΅ 40 % of p = 23040 β΄ p = ( 23040 x 100 ) / 40 = 57600 correct option : a" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"290 / 289",
"122 / 121",
"290 / 90",
"290 / 19"
]
} | [
"B"
] | product of two natural numbers is 11 . then , the sum of reciprocals of their squares is | "explanation : if the numbers are a , b , then ab = 17 , as 17 is a prime number , so a = 1 , b = 17 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 11 ( 2 ) = 122 / 121 option b" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1240",
"1120",
"1190",
"1978"
]
} | [
"D"
] | the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 828 . what is the banker ' s discount ? | "explanation : td = ( bg Γ 100 ) / tr = ( 828 Γ 100 ) / ( 6 Γ 12 ) = rs . 1150 bg = bd β td = > 828 = bd - 1150 = > bd = 1978 answer : option d" | MathQA |
{
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"8000000",
"1000000",
"7500000",
"1200000"
]
} | [
"A"
] | a wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 2 cm x 7 cm x 3 cm . the maximum number ofboxes that can be carried in the wooden box , is | explanation : number = ( 800 * 700 * 600 ) / 2 * 7 * 3 = 8000000 answer : a | MathQA |
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