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MNLP_M3_mathqa

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{ "label": [ "A", "B", "C", "D" ], "text": [ "1.2 kg", "1.5 kg", "1.7 kg", "1.9 kg" ] }
[ "C" ]
when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 15 % water ?
"explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 85 % ( 100 - 15 ) . therefore 0.5 x amount of flower - nectar = 0.85 x amount of honey = 0.85 x 1 kg therefore amount of flower - nectar needed = ( 0.85 / 0.51 ) kg = 1.7 kgs answer : c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "180", "176", "175", "96" ] }
[ "A" ]
a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 270 metres long in 20 seconds . the length of the train ( in metres ) is :
"explanation : let the length of train be l m . acc . to question ( 270 + l ) / 20 = l / 8 2160 + 8 l = 20 l l = 2160 / 12 = 180 m answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4 m", "4.5 m", "5 m", "6 m" ] }
[ "A" ]
the heights of a wall is 6 times its width and the length of the wall is 7 times its height . if volume of the wall be 16128 cu . m , its width is
solution let the width of the wall be x metres . then , height = ( 6 x ) m and length = ( 42 x ) m . 42 x Γ— x Γ— 6 x = 16128 x 3 β€Ή = β€Ί ( 16128 / 42 Γ— 6 ) = 64 β€Ή = β€Ί x = 4 . answer a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "20 hours", "24 hours", "26 hours", "18 hours" ] }
[ "B" ]
a cistern normally takes 6 hours to be filled by a tap but because of a leak , 2 hours more . in how many hours will the leak empty a full cistern ?
∡ cistern fill in 6 hours . ∴ in 1 hour , filled part = 1 ⁄ 6 th now , due to leakage , filled part in 1 hour = 1 ⁄ 8 th part of the cistern emptied , due to leakage in 1 hour = 1 ⁄ 6 - 1 ⁄ 8 = 1 ⁄ 24 th ∴ the leakage will empty the full cistern in 24 hrs . answer b
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4500", "7500", "5000", "6800" ] }
[ "D" ]
the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 17 . 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 βˆ’ 100100 ( 1 + 5100 ) 2 βˆ’ 100 ∴ = 100 Γ— 21 Γ— 2120 Γ— 20 βˆ’ 100 = 414 = 100 Γ— 21 Γ— 2120 Γ— 20 βˆ’ 100 = 414 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the d...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "120", "100", "125", "150" ] }
[ "B" ]
the difference between a number and its three - fourth is 100 . what is 25 % of that number ?
"explanation : solution : let the number be x . then , x - 3 / 4 x = 100 = > x / 4 = 100 = > x = 400 . 25 % of x = 25 % of 400 = 25 / 100 * 400 = 100 . answer : b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2 : 3", "7 : 40", "3 : 20", "20 : 3" ] }
[ "B" ]
if 0.4 of a number is equal to 0.07 of another number , the ratio of the numbers i
"sol . 0.4 a = 0.08 b Γ’ ‑ ” a / b = 0.07 / 0.40 = 7 / 40 . Γ’ Λ† Β΄ a : b = 7 : 40 . answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "16 , 35,36", "12 , 28,36", "16 , 28,27", "16 , 28,36" ] }
[ "D" ]
ratio of ages of 3 persons is 4 : 7 : 9 , 8 years ago , the sum of their ages was 56 . find their present ages
explanation : let the present ages are 4 x , 7 x , 9 x . = > ( 4 x - 8 ) + ( 7 x - 8 ) + ( 9 x - 8 ) = 56 = > 20 x = 80 = > x = 4 so their present ages are : 16 , 28,36 answer : option d
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "7580", "7960", "8290", "8640" ] }
[ "D" ]
a leak in the bottom of a tank can empty the full tank in 8 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
"solution work done by the inlet in 1 hour = ( 1 / 8 - 1 / 12 ) = 1 / 24 . work done by the inlet in 1 min . = ( 1 / 24 Γ— 1 / 60 ) = 1 / 1440 . volume of 1 / 1440 part = 6 litres . therefore , volume of whole = ( 1440 Γ— 6 ) β€Ή = β€Ί 8640 litres . answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "365", "52", "1024", "8760" ] }
[ "D" ]
how many hours in one year ?
the day has 24 hours , and the year contains 365 days . so the hours exist in one year is the multiplication of 24 by 365 . so the answer = 365 * 24 = 8760 hours so the correct answer is d
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4500", "7500", "5000", "6400" ] }
[ "D" ]
the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 16 . find the sum :
"sol . ( d ) let the sum be 100 . therefore , si = 100 Γ— 5 Γ— 2 / 100 = 10 and ci = 100 ( 1 + 5 / 100 ) 2 βˆ’ 100 ∴ = 100 Γ— 21 Γ— 21 / 20 Γ— 20 βˆ’ 100 = 41 / 4 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 16 , the sum = 400 Γ— 16 = 6400 answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "8 : 5', '", "9 : 25', '", "5 : 8', '", "25 : 9', '" ] }
[ "C" ]
two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 80 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 40 ...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "10.22 %", "20.22 %", "21.22 %", "40 %" ] }
[ "D" ]
a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 40 % while buying and by 10 % while selling . what is his percentage profit ?
"the owner buys 100 kg but actually gets 140 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 140 - 90 ) / 90 * 100 = 40 % answer : d ."
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4 : 3", "3 : 5", "3 : 4", "50 : 3" ] }
[ "C" ]
a track covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minute . the ratio of their speeds is :
solution : speed of track = 550 per minute . speed of bus = 33 kms / 45 = 33000 / 45 = 733.33 m / minute ratio of their speeds = 550 / 733.33 = 3 : 4 . answer : option c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "0 Β°", "5 Β°", "10 Β°", "20 Β°" ] }
[ "C" ]
the angle between the minute hand and the hour hand of a clock when the time is 4.20 Β° is
"sol . angle traced by hour hand in 13 / 3 hrs = ( 360 / 12 x 13 / 3 ) ° = 130 ° angle traced by min . hand in 20 min . = ( 360 / 60 x 20 ) ° = 120 ° ∴ required angle = ( 130 - 120 ) ° = 10 ° answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "3 : 4", "3 : 5", "4 : 5", "16 : 15" ] }
[ "D" ]
a man invests some money partly in 9 % stock at 96 and partly in 12 % stock at 120 . to obtain equal dividends from both , he must invest the money in the ratio :
"solution for an income of rs . 1 in 9 % stock at 96 , investment = rs . ( 96 / 9 ) = rs . 32 / 3 . for an income of rs . 1 in 12 % stock at 120 , investment = rs . ( 120 / 12 ) = rs . 10 . ∴ ratio of investments = 32 / 3 : 10 = 32 : 30 = 16 : 15 answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1.25", "5.75", "3.25", "3.75" ] }
[ "D" ]
1 , 0.5 , 0.5 , 0.75 , 1.5 , ____
"1 , 0.5 , 0.5 , 0.75 , 1.5 , . . . . . 1 * 0.5 = 0.5 0.5 * 1 = 0.5 0.5 * 1.5 = 0.75 0.75 * 2 = 1.5 so , 1.5 * 2.5 = 3.75 answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 2000", "rs . 1750", "rs . 2010", "rs . 2005" ] }
[ "B" ]
find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 2030 ?
"explanation : 2030 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1750 answer : option b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "20,20", "20,10", "25,15", "35,11" ] }
[ "D" ]
the ages of two persons differ by 24 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
"explanation : let their ages be x and ( x + 24 ) years . 5 ( x - 5 ) = ( x + 24 - 5 ) or 4 x = 44 or x = 11 . their present ages are 35 years and 11 years option d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "15", "16", "18", "20" ] }
[ "A" ]
the difference of two numbers is 20 % of the larger number . if the smaller number is 12 , the larger one is :
"let the larger number be x . then , x - 12 = 20 % of x < > x - ( x / 5 ) = 12 4 x / 5 = 12 < = > x = ( 12 βˆ— 5 ) / 5 = 15 . answer : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "5 %", "10 %", "15 %", "20 %" ] }
[ "A" ]
a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 45 % have red flags , what percentage of children have flags of bo...
"solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 45 % = 45...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4", "7", "8", "10" ] }
[ "D" ]
64 Γ£ β€” 64 Γ£ β€” 64 Γ£ β€” 64 x 64 = 8 ^ ?
"64 Γ£ β€” 64 Γ£ β€” 64 Γ£ β€” 64 x 64 = 8 ^ ? or , 8 ( 2 ) Γ£ β€” 8 ( 2 ) Γ£ β€” 8 ( 2 ) Γ£ β€” 8 ( 2 ) x 8 ( 2 ) = 8 ? or 7 ( 10 ) = 8 ? or , ? = 10 answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "3.45", "4.5", "2.25", "3.21" ] }
[ "A" ]
the simple interest on rs . 23 for 3 months at the rate of 5 paise per rupeeper month is
sol . s . i . = rs . [ 23 * 5 / 100 * 3 ] = rs . 3.45 answer a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "76", "5776", "304", "2704" ] }
[ "D" ]
find √ ? / 13 = 4 ?
"answer let √ n / 13 = 4 then √ n = 13 x 4 = 52 ∴ n = 52 x 52 = 2704 . correct option : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "36 kmph", "40 kmph", "30 kmph", "42 kmph" ] }
[ "A" ]
a goods train leaves a station at a certain time and at a fixed speed . after 6 hours , an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph . this train catches up the goods train in 4 hours . find the speed of the goods train .
let the speed of the goods train be x kmph . distance covered by goods train in 10 hours = distance covered by express train in 4 hours . ∴ 10 x = 4 Γ— 90 or x = 36 . so , speed of goods train = 36 kmph . answer a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "340", "342", "523", "363" ] }
[ "B" ]
the least number which when divided by 4 , 6 , 7 and 8 leaves a remainder 6 , but when divided by 9 leaves no remainder , is
"explanation : l . c . m of 4 , 6 , 7 , 8 = 168 therefore required number is of the form 168 k + 6 . least value of k for which ( 168 k + 6 ) is divisible by 9 is k = 2 therefore required number = ( 168 x 2 + 6 ) = 342 . answer : b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "56", "5.6", "0.56", "0.056" ] }
[ "B" ]
if 0.6 : 1.4 : : 2 : 4 : x , then x = ?
"explanation : 0.6 Γ— x = 2.4 Γ— 1.4 x = ( 2.4 Γ— 1.4 ) / 0.6 = 24 / 10 Γ— 17 / 10 Γ— 1 / ( 6 / 10 ) 24 / 10 Γ— 14 / 10 Γ— 10 / 6 2 / 5 Γ— 14 = 28 / 5 = 5.6 answer : option b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2 %", "5 %", "6 %", "8.75 %" ] }
[ "A" ]
the population of a town increased from 1 , 75,000 to 2 , 10,000 in a decade . the average percent increase of population per year is
"solution increase in 10 years = ( 210000 - 175000 ) = 35000 . increase % = ( 35000 / 175000 Γ£ β€” 100 ) % = 20 % . required average = ( 20 / 10 ) % = 2 % . answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 200', '", "rs . 672', '", "rs . 546', '", "rs . 876', '" ] }
[ "A" ]
the cost of the paint is rs . 20 per kg . if 1 kg of paint covers 15 sq . ft , how much will it cost to paint outside of a cube having 5 feet each side
explanation : surface area of a cube = 6 x 5 ^ 2 = 150 sq . ft quantity of paint required = ( 150 / 15 ) = 10 kg cost of painting = 20 x 10 = rs . 200 answer : a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "12.5 %", "40 %", "80 %", "125 %" ] }
[ "D" ]
the ratio 5 : 4 expressed as a percent equals
"solution 5 : 4 = 5 / 4 = ( 5 / 4 x 100 ) % . = 125 % . answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "0.0584", "0.0484", "0.0434", "0.0384" ] }
[ "D" ]
1 , 0.2 , 0.08 , 0.48 , 0.0384 , ____
"1 , 0.2 , 0.08 , 0.48 , 0.0384 , . . . . . 1 * 0.2 = 0.2 0.2 * 0.4 = 0.08 0.08 * 0.6 = 0.048 0.048 * 0.8 = 0.0384 so 0.0384 * 1 = 0.0384 answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "256", "4", "√ 2", "16" ] }
[ "A" ]
( 5568 / 87 ) 1 / 3 + ( 72 x 2 ) 1 / 2 = ( ? ) 1 / 2 ?
answer ? ) 1 / 2 = ( 5568 / 87 ) 1 / 3 + ( 72 x 2 ) 1 / 2 = ( 64 ) 1 / 3 + ( 144 ) 1 / 2 ∴ ? = ( 4 + 12 ) 2 = 256 correct option : a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "60 %", "40 %", "80 %", "125 %" ] }
[ "A" ]
the ratio 3 : 5 expressed as a percent equals
"solution 3 : 5 = 3 / 5 = ( 3 / 5 x 100 ) % . = 60 % . answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "108.45", "110.45", "106.45", "109.45" ] }
[ "A" ]
solve : 12.05 * 5.4 + 0.6
= 12.05 * ( 5.4 / 0.6 ) = ( 12.05 * 9 ) = 108.45 answer is a .
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "10", "20", "30", "40" ] }
[ "B" ]
in the new budget , the price of kerosene oil rose by 25 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?
reduction in consumption = [ ( ( r / ( 100 + r ) ) * 100 ] % = [ ( 25 / 125 ) * 100 ] % = 20 % . answer is b .
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "5 : 2", "2 : 1", "11 : 7", "13 : 9" ] }
[ "B" ]
the ration of the father ’ s age to his son ’ s age is 7 : 3 . the product of their ages is 756 . the ratio of their ages after 6 years will be :
solution let the present ages of the father and son be 7 x and 3 x years respectively . then , 7 x 3 x = 756 ⇔ 21 x 2 = 756 ⇔ x 2 = 36 ⇔ x = 6 . ∴ required ratio = ( 7 x + 6 ) : ( 3 x + 6 ) = 48 : 24 = 2 : 1 . answer b
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 72", "rs . 36", "rs . 54", "rs . 50" ] }
[ "D" ]
the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 6 . the true discount is
"solution t . d = [ b . g x 100 / r x t ] = rs . ( 6 x 100 / 12 x 1 ) = rs . 50 . answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "24", "25", "48", "50" ] }
[ "A" ]
the average of 30 results is 20 and the average of other 20 results is 30 . what is the average of all the results ?
"answer sum of 50 result = sum of 30 result + sum of 20 result . = 30 x 20 + 20 x 30 = 1200 correct option : a"
MathQA
{ "label": [ "A", "B", "D", "E" ], "text": [ "1", "1 / 2", "2", "- 1" ] }
[ "D" ]
if | x | = 7 x - 5 , then x = ?
"answer : a approach : substituted option a i . e x = 1 . inequality satisfied . d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "148", "154", "156", "144" ] }
[ "B" ]
the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 150 . what is the number of frogs in the pond ?
"solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 150 . so , total number of ducks and frogs in the pond , = 2 * 150 = 300 . therefore , number of frogs , = ( 300 * 39 ) / 76 = 154 . answer : option b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 420000", "rs . 180000", "rs . 201600", "rs . 470400" ] }
[ "D" ]
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 . 14000 , then find the annual income of a ?
"b ' s monthly income = 14000 * 112 / 100 = rs . 15680 b ' s monthly income = 2 parts - - - - > rs . 15680 a ' s monthly income = 5 parts = 5 / 2 * 15680 = rs . 39200 a ' s annual income = rs . 39200 * 12 = rs . 470400 answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2", "4", "8", "16" ] }
[ "A" ]
in the rectangular coordinate system , points ( 2 , 0 ) and ( – 2 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
"the answer is a it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreate...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "26.4 %", "21 %", "20 %", "19 %" ] }
[ "A" ]
mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 457 ?
"cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 457 , discount = 621 - 457 = 164 discount % = 164 / 621 * 100 = 26.4 % answer : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "699990", "99990", "99980", "69300" ] }
[ "D" ]
what is the difference between the place values of two sevens in the numeral 54179759 ?
explanation : required difference = 70000 - 700 = 69300 answer is d
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 9313.34", "rs . 9720", "rs . 10123.20", "rs . 10483.20" ] }
[ "A" ]
what will be the compound interest on a sum of rs . 23,000 after 3 years at the rate of 12 % p . a . ?
"amount = [ 23000 * ( 1 + 12 / 100 ) 3 ] = 23000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 32313.34 c . i . = ( 32313.34 - 23000 ) = rs . 9313.34 answer : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "11.59 %", "12.59 %", "13.59 %", "14.59 %" ] }
[ "B" ]
a shopkeeper fixes the marked price of an item 25 % above its cost price . the percentage of discount allowed to gain 8 % is
"explanation : let the cost price = rs 100 then , marked price = rs 125 required gain = 8 % , so selling price = rs 108 discount = 125 - 108 = 17 discount % = ( 17 / 135 ) * 100 = 12.59 % option b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs 1650", "rs 1750", "rs 1850", "rs 1950" ] }
[ "B" ]
simple interest on a certain sum of money for 3 years at 8 % per annum is half the compound interest on rs . 4000 for 2 years at 10 % per annum . the sum placed on simple interest is
"explanation : c . i . = ( 4000 Γ— ( 1 + 10 / 100 ) 2 βˆ’ 4000 ) = 4000 βˆ— 11 / 10 βˆ— 11 / 10 βˆ’ 4000 = 840 so s . i . = 840 / 2 = 420 so sum = s . i . βˆ— 100 / r βˆ— t = 420 βˆ— 100 / 3 βˆ— 8 = rs 1750 option b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1 : 2", "6 : 9", "4 : 5", "2 : 3" ] }
[ "C" ]
if the ratio of s . i earned on certain amount on same rate is 4 : 5 . what is the ratio of time ?
s . i 1 / s . i 2 = [ ( p * r * t 1 ) / 100 ] / [ ( p * r * t 2 ) / 100 ] 4 / 5 = t 1 / t 2 ratio = 4 : 5 answer c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 30,000", "rs . 50,000", "rs . 60,000", "rs . 100,000" ] }
[ "D" ]
one - third of rahul ’ s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 2 , 50000 as total savings , how much has he saved in public provident fund ?
explanation let savings in n . s . c and p . p . f . be rs . x and rs . ( 250000 – x ) respectively . then , 1 / 3 x = 1 / 2 ( 250000 - x ) = > x / 3 + x / 2 = 125000 = > 5 x / 6 = 125000 = > x = 125000 x 6 / 5 = 150000 savings in public provident fund = rs . ( 250000 – 150000 ) = rs . 100000 answer d
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "15 %", "25 %", "12.5 %", "20.83 %" ] }
[ "D" ]
farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 4000 through the farm tax from the village of mr . willam . mr . willam paid only $ 500 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
"only trick n this question is to ignore 60 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to (...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1.5 kmph", "1.75 kmph", "2 kmph", "3 kmph" ] }
[ "A" ]
a man rows downstream 32 km and 14 km upstream . if he takes 6 hours to cover each distance , then the velocity ( in kmph ) of the current is :
sol . rate downstream = [ 32 / 6 ] kmph ; rate upstream = [ 14 / 6 ] kmph . ∴ velocity of current = 1 / 2 [ 32 / 6 - 14 / 6 ] kmph = 3 / 2 kmph = 1.5 kmph . answer a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "5 kg", "15 kg", "25 kg", "30 kg" ] }
[ "C" ]
the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?
"solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 20 % , new price for 20 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 20 = rs . 4 per kg . rice can bought now at = 100 / 4 = 25 kg . answer : option c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2 mph", "2.5 mph", "3 mph", "4 mph" ] }
[ "A" ]
a boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream . if the speed of the boat in still water is 10 mph , the speed of the stream is
"solution speed downstreams = ( 10 + x ) mph . speed upstreams = ( 10 - x ) mph . = 18 kmph . 36 / ( 10 - x ) - 36 / ( 10 + x ) = 90 / 60 = 72 x Γ— 60 = 90 ( 100 - x Β² ) x Β² + 48 x + 100 = 0 . x = 2 mph . answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2984", "2983", "2982", "2450" ] }
[ "D" ]
2500 - ( 1002 / 20.04 ) = ?
"2500 - 50 = 2450 answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "30", "36", "34", "32" ] }
[ "D" ]
24 men working 8 hours a day can finish a work in 10 days . working at the rate of 10 hours a day , the number of men required to finish the same work in 6 days is
m 1 Γ— d 1 Γ— t 1 Γ— w 2 = m 2 Γ— d 2 Γ— t 2 Γ— w 1 24 Γ— 10 Γ— 8 Γ— 1 = m 2 Γ— 6 Γ— 10 Γ— 1 β‡’ m 2 = 24 Γ— 10 Γ— 8 / 6 Γ— 10 = 32 men answer d
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 13.44", "rs . 12", "rs . 12.25", "rs . 12.31" ] }
[ "A" ]
a fruit seller sells mangoes at the rate of rs . 11 per kg and thereby loses 10 % . at what price per kg , he should have sold them to make a profit of 10 % ?
"solution 90 : 11 = 110 : x x = ( 11 Γ£ β€” 110 / 90 ) = rs . 13.44 hence , s . p per kg = rs . 13.44 answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 1800", "rs . 1450", "rs . 1360", "rs . 6800" ] }
[ "C" ]
the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 85 and rs . 80 respectively . the sum is :
"solution sum = s . i xt . d / ( s . i ) - ( t . d ) = 85 x 80 / 85 - 80 = rs . 1360 . answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "9801", "10,000", "14,400", "12,696" ] }
[ "A" ]
a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 197 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many...
"let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 197 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 197 ( x + y ) ( x - y ) = 197 197 is a prime number and thus ...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 420000", "rs . 403200", "rs . 201600", "rs . 504000" ] }
[ "B" ]
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 . 12000 , then find the annual income of a ?
"b ' s monthly income = 12000 * 112 / 100 = rs . 13440 b ' s monthly income = 2 parts - - - - > rs . 13440 a ' s monthly income = 5 parts = 5 / 2 * 13440 = rs . 33600 a ' s annual income = rs . 33600 * 12 = rs . 403200 answer : b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "28.5", "27.675", "30", "50" ] }
[ "D" ]
a shopkeeper sold an article offering a discount of 5 % and earned a profit of 42.5 % . what would have been the percentage of profit earned if no discount had been offered ?
"giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 Γ£ β€” ( 100 + 42.5 ) / ( 100 Γ’ Λ† ’ 5 ) = 150 hence , required % profit = 150 Γ’ € β€œ 100 = 50 % answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "586413", "587523", "614823", "615173" ] }
[ "A" ]
587 x 999 = ?
"= 587 x 999 = 587 x ( 1000 - 1 ) = 587 x 1000 - 587 - 1 = 587000 - 587 = 586413 answer is a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2.6 hours", "3.6 hours", "4.6 hours", "5.6 hours" ] }
[ "B" ]
a tank can be filled by pipe a in 5 hours and by pipe b in 8 hours , each pump working on its own . when the tank is full and a drainage hole is open , the water is drained in 20 hours . if initially the tank was empty and someone started the two pumps together but left the drainage hole open , how long does it take fo...
let ' s first find the rates of the pumps and the drainage hole pump a : 1 / 5 , pump b : 1 / 8 , drainage hole : 1 / 20 let t be the time for the pumps to fill the tank . the pumps , add water into the tank however the drainage hole drains water out of the tank , hence t ( 1 / 5 + 1 / 8 - 1 / 20 ) = 1 solve for t t = ...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2 : 1", "14 : 3", "7 : 2", "1 : 2" ] }
[ "A" ]
if a : b : c = 3 : 4 : 7 , then the ratio ( a + b + c ) : c is equal to
solution : ( a + b + c ) = 3 + 4 + 7 = 14 and c = 7 then , ( a + b + c ) : c = 2 : 1 . answer : option a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2", "4", "5", "500" ] }
[ "A" ]
45 x ? = 10 % of 900
answer let 45 x a = ( 10 x 900 ) / 100 ∴ a = ( 10 x 9 ) / 45 = 2 correct option : a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "0", "1", "2", "3" ] }
[ "A" ]
if z is a multiple of 9702 , what is the remainder when z ^ 2 is divided by 4 ?
"2 is a factor of 9702 , so 2 is a factor of z . then 2 ^ 2 = 4 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 4 is 0 . the answer is a ."
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "225", "500", "75", "800" ] }
[ "A" ]
a and b undertake to do a piece of work for rs . 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . ! find the share of b .
"c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 Β» ) = rs . 75 . answer is a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "28000", "30000", "32000", "34000" ] }
[ "A" ]
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 4000 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 = 4000 = > total profit = 4000 * 7 = 28000 . answer : option a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "12", "39", "54", "156" ] }
[ "D" ]
the mean proportional between 234 and 104 is
"sol . required mean proportional = √ 234 x 104 = √ 13 x 9 x 2 x 13 x 8 = ( 13 x 3 x 4 ) = 156 . answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "28 : 15", "29 : 16", "25 : 23", "14 : 15" ] }
[ "A" ]
x starts a business with rs . 35000 . y joins in the business after 3 months with rs . 25000 . what will be the ratio in which they should share the profit at the end of the year ?
"explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 35000 * 12 : 25000 * 9 = 35 * 12 : 25 * 9 = 7 * 4 : 5 * 3 = 28 : 15 . answer : option a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2200 kmph", "1800 kmph", "1900 kmph", "2100 kmph" ] }
[ "B" ]
an aeroplane covers a certain distance at a speed of 1500 kmph in 2 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
"explanation : distance = ( 1500 x 2 ) = 3000 km . speed = distance / time speed = 3000 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = 3000 x 3 / 5 km / hr = 1800 km / hr . answer : option b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "βˆ’ 220", "βˆ’ 100", "100", "110" ] }
[ "D" ]
if the average ( arithmetic mean ) of a and b is 215 , and the average of b and c is 160 , what is the value of a βˆ’ c ?
"question : a - c = ? ( a + b ) / 2 = 215 = = = > a + b = 430 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 430 - 320 = = = > a + b - b - c = 110 = = = > a - c = 110 answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1.2 %", "2 %", "4 %", "5 %" ] }
[ "D" ]
at what rate percent per annum will sum of money double in 20 years ?
"explanation : hint : if sum of money becomes ( z times ) in ( t ) years at simple interest , then rate of interest ( r ) can be calculated using the formula : rate of interest ( r ) % = 100 ( z – 1 ) / t here , principal amount is not given . hence , we can directly use the trick to calculate the rate of interest . ra...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "3427", "3237", "3337", "2337" ] }
[ "A" ]
9773 + x = 13200 , then x is ?
"answer x = 13200 - 9773 = 3427 option : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "124 m 2", "128 m 2", "138 m 2", "148 m 2" ] }
[ "D" ]
the floor of a rectangular room is 21 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :
"area of the outer rectangle = 25 Γ£ β€” 16 = 400 m 2 area of the inner rectangle = 21 Γ£ β€” 12 = 252 m 2 required area = ( 400 Γ’ € β€œ 252 ) = 148 m 2 answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "41 / 25", "15 / 14", "4 / 5", "5 / 4" ] }
[ "A" ]
jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 2.5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
"average speed of jack = distance / time = 42 / ( 5 / 2 ) = 84 / 5 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 84 / 5 ) / 10 = 84 / 50 = 41 / 25 answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "49 th", "48 th", "47 th", "50 th" ] }
[ "A" ]
jaya ranks 5 th in a class of 53 . what is her rank from the bottom in the class ?
there are 4 students above her . when takan from bottom there are 4 students below her rank . so her rank wud be 53 - 4 i . e . 49 th . answer : a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "7.2 kg .", "10.8 kg .", "14.04 kg .", "18.0 kg" ] }
[ "C" ]
if the weight of 10 meters long rod is 23.4 kg . what is the weight of 6 meters long rod ?
"answer ∡ weight of 10 m long rod = 23.4 kg ∴ weight of 1 m long rod = 23.4 / 10 kg ∴ weight of 6 m long rod = 23.4 x 6 / 10 = 14.04 kg option : c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1936372", "2029272", "1896172", "1923472" ] }
[ "B" ]
2056 x 987 = ?
"= 2056 x 987 = 2056 x ( 1000 - 13 ) = 2056 x 1000 - 2056 x 13 = 2056000 - 26728 = 2029272 answer is b"
MathQA
{ "label": [ "A", "C", "D", "E" ], "text": [ "1 hour", "3 hours", "2 hours 30 min", "2 hours" ] }
[ "C" ]
a train is moving at 6 / 7 of its usual speed . the train is 30 minutes too late . what is the usual time for the train to complete the journey ?
"new time = d / ( 6 v / 7 ) = 7 / 6 * usual time 30 minutes represents 1 / 6 of the usual time . the usual time is 3 hours . the answer is c ."
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2.29", "2.75", "4.25", "4.5" ] }
[ "D" ]
( 17 ) 3.5 x ( 17 ) ? = 178
"solution let ( 17 ) 3.5 * ( 17 ) x = 178 . then , ( 17 ) 3.5 + x = ( 17 ) 8 . ∴ 3.5 + x = 8 ⇔ x = ( 8 - 3.5 ) ⇔ x = 4.5 answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "15", "24", "17", "19" ] }
[ "B" ]
excluding stoppages , the speed of a bus is 75 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
"due to stoppages , it covers 30 km less . time taken to cover 30 km = ( ( 30 / 75 ) Γ£ β€” 60 ) = 24 min . option ( b ) is correct"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "r = 300", "r = 400", "r = 500", "600" ] }
[ "C" ]
there are 200 female managers in a certain company . find the total number r of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
"{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "100 m", "120 m", "130 m", "150 m" ] }
[ "C" ]
a policeman noticed a criminal from a distance of 180 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ?
explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 180 - 50 ) m = 130 m . answer : c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "15 m Γ— 6.67 m', '", "20 m Γ— 5 m', '", "30 m Γ— 3.33 m', '", "40 m Γ— 2.5 m', '" ] }
[ "B" ]
a farmer wishes to start a 100 square metres rectangular vegetable garden . since he has only 30 m barbed wire , he fences three sides of the garden letting his house compound wall act as the fourth side fencing . the dimension of the garden is :
we have : 2 b + l = 30 β‡’ l = 30 – 2 b . area = 100 m 2 β‡’ l Γ— b = 100 β‡’ b ( 30 – 2 b ) = 100 β‡’ b 2 – 15 b + 50 = 0 β‡’ ( b – 10 ) ( b – 5 ) = 0 β‡’ b = 10 or b = 5 . when b = 10 , l = 10 and when b = 5 , l = 20 . since the garden is rectangular , so its dimension is 20 m Γ— 5 m . answer b
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "26", "27", "46", "57" ] }
[ "B" ]
the sum of three 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 ⇔ 9 x = 63 ⇔ x = 7 . ∴ largest number = 3 x + 6 = 27 . answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "0.3408", "3.408", "34.08", "340.8" ] }
[ "C" ]
if 213 Γ— 16 = 3408 , then 1.6 Γ— 21.3 is equal to :
"solution 1.6 Γ— 21.3 = ( 16 / 10 x 213 / 10 ) = ( 16 x 213 / 100 ) = 3408 / 100 = 34.08 . answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1200", "1764", "1400", "1354" ] }
[ "C" ]
the true discount on a bill due 9 months hence at 16 % per annum is rs . 150 . the amount of the bill is
explanation : let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 150 . x Γ£ β€” 16 Γ£ β€” ( 9 / 12 ) Γ£ β€” ( 1 / 100 ) = 150 or x = 1250 . p . w . = rs . 1250 sum due = p . w . + t . d . = rs . ( 1250 150 ) = rs . 1400 answer : c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 115", "rs . 116", "rs . 117", "rs . 118" ] }
[ "C" ]
9 persons went to a hotel for taking their meals . 8 of them spent rs . 12 each on their meals and the ninth spent rs . 8 more than the average expenditure of all the 9 . what was the total money spent by them .
solution : let the average expenditure of all the nine be x . then , 12 Γ— 8 + ( x + 8 ) = 9 x . therefore , x = 13 . total money spent , = 9 x = rs . ( 9 Γ— 13 ) = rs . 117 answer : option c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1 : 25", "1 : 36", "1 : 52", "1 : 522" ] }
[ "B" ]
a cube of edge 6 cm is cut into cubes each of edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
"sol . required ratio = 6 * 1 * 1 / 6 * 6 * 6 = 1 / 36 = 1 : 36 . answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 432", "rs . 422", "rs . 412", "rs . 442" ] }
[ "B" ]
the true discount on a bill of rs . 2460 is rs . 360 . what is the banker ' s discount ?
"explanation : f = rs . 2460 td = rs . 360 pw = f - td = 2460 - 360 = rs . 2100 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2100 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 500", "rs . 1400", "rs . 2000", "rs . 2500" ] }
[ "B" ]
a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 700 more than d , what is b ' s share ?
"let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 700 x = 700 . b ' s share = rs . 2 x = rs . ( 2 x 700 ) = rs . 1400 . answer = b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "900", "800", "600", "300" ] }
[ "D" ]
if 90 % of a = 30 % of b and b = c % of a , then the value of c is ?
"answer ∡ 90 a / 100 = 30 b / 100 = ( 30 / 100 ) x ac / 100 ∴ c = 100 x ( 100 / 30 ) x ( 90 / 100 ) = 300 correct option : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "84', '", "86', '", "82', '", "80', '" ] }
[ "A" ]
the inner circumference of a circular race track , 14 m wide , is 440 m . find radius of the outer circle .
let inner radius be r metres . then , 2 ( 22 / 7 ) r = 440 = r = ( 440 x ( 7 / 44 ) ) = 70 m . radius of outer circle = ( 70 + 14 ) m = 84 m . answer is a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 10,000", "rs . 10,800", "rs . 14,400", "rs . 16,000" ] }
[ "A" ]
to produce an annual income of rs . 1200 from a 12 % stock at 90 , the amount of stock needed is :
solution for an income of rs . 12 , stock needed = rs . 100 . for an income of rs . 1200 , stock needed = rs . 100 / 12 x 1200 = 10000 answer a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "960", "975", "1,200", "920" ] }
[ "B" ]
the profit earned by selling an article for 852 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 852 – x = 448 + x or , x = 404 ⁄ 2 = 202 \ cost price of the article = 852 – x = 448 + x = 650 \ sp of the article = 650 Γ— 150 ⁄ 100 = 975 answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 147.50", "rs . 785.50", "rs . 179.50", "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 157 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...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "79.2 km / hr", "69 km / hr", "74 km / hr", "61 km / hr" ] }
[ "B" ]
a train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively . what is the speed of the train ?
let x is the length of the train and v is the speed time taken to move the post = 8 s = > x / v = 8 = > x = 8 v - - - ( 1 ) time taken to cross the platform 264 m long = 20 s ( x + 264 ) / v = 20 = > x + 264 = 20 v - - - ( 2 ) substituting equation 1 in equation 2 , we get 8 v + 264 = 20 v = > v = 264 / 12 = 22 m / s =...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 1075", "rs . 975", "rs . 875", "rs . 775" ] }
[ "C" ]
find the simple interest on rs 7000 at 50 / 3 % for 9 months
"explanation : s . i . = p Γ— r Γ— t 100 so , by pu Ζ« ing the values in the above formula , our result will be . required result = 7000 Γ— 50 Γ— 93 Γ— 12 Γ— 100 = 875 [ please note that we have divided by 12 as we converted 9 months in a year format ] answer : c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "$ 21", "$ 27", "$ 31", "$ 39" ] }
[ "D" ]
at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 160.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
"let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 160.5 subtracting the first equation from the second gives us b + 3 s = 40.5 now if we subtract the new equation two times from first or 3 times fro...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "15060000", "0.001506", "0.01506", "0.1506" ] }
[ "B" ]
15.06 * 0.0001 = ?
"explanation : clearly after decimal 6 digits should be there . option b"
MathQA