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MNLP_M3_mathqa

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{ "label": [ "A", "B", "C", "D" ], "text": [ "11", "15", "13", "14" ] }
[ "B" ]
15 times a number gives 150 . the number is
explanation : let the number be ' n ' 15 Γ— n = 150 β‡’ n = 10 correct option : b
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 3000", "rs . 1600", "rs . 2400", "rs . 4000" ] }
[ "B" ]
p , q and r have rs . 4000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
"let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 4000 - r ) = > 3 r = 8000 - 2 r = > 5 r = 8000 = > r = 1600 . answer : b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 700", "rs . 780", "rs . 750", "rs . 1000" ] }
[ "C" ]
find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 870 ?
"explanation : 870 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 750 answer : option c"
MathQA
{ "label": [ "A", "B", "C", "E" ], "text": [ "54210", "54250", "52150", "521500" ] }
[ "C" ]
( 32323 + 7344 + 41330 ) - ( 317 x 91 ) = ?
"its speed and accuracy which decides the winner . you can use various methods including vedic mathematics to do complex calculations quickly . ( 32323 + 7344 + 41330 ) - ( 317 x 91 ) = 80997 - 28847 = 52150 answer is c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "15", "11", "28", "91" ] }
[ "B" ]
if the sum of a number and its square is 132 , what is the number ?
let the number be x . then , x + x 2 = 132 ( x + 12 ) ( x - 11 ) = 0 x = 11 answer : b
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "10.22 %", "20.22 %", "21.22 %", "22.22 %" ] }
[ "D" ]
a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 10 % while buying and by 10 % while selling . what is his percentage profit ?
"the owner buys 100 kg but actually gets 110 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 110 - 90 ) / 90 * 100 = ~ 22.22 % answer : d ."
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "46.2 %", "54.54 %", "60.52 %", "70 %" ] }
[ "C" ]
a cricketer scored 152 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
"explanation : number of runs made by running = 152 - ( 12 x 4 + 2 x 6 ) = 152 - ( 60 ) = 92 now , we need to calculate 92 is what percent of 152 . = > 92 / 152 * 100 = 60.52 % answer : c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4000", "3000", "5500", "4500" ] }
[ "A" ]
a profit of rs . 20000 is to be distributed among a , b , c in the proportion 2 : 3 : 5 . what will be the difference between b ’ s and c ’ s shares
explanation : b ' s share = rs 20000 * ( 3 / 10 ) = rs 6000 c ' s share = rs 20000 * ( 5 / 10 ) = rs 10000 difference in b ' s and c ' s shares = rs 4000 answer : a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4.37 %", "5 %", "6 %", "8.75 %" ] }
[ "B" ]
the population of a town increased from 1 , 75,000 to 2 , 62,500 in a decade . the average percent increase of population per year is
"solution increase in 10 years = ( 262500 - 175000 ) = 87500 . increase % = ( 87500 / 175000 Γ— 100 ) % = 50 % . required average = ( 50 / 10 ) % = 5 % . answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 1 , 10,000", "rs . 1 , 20,000", "rs . 1 , 22,000", "rs . 1 , 21,000" ] }
[ "C" ]
the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 26,000 is made ?
"the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 24,000 is made = 96,000 + 26,000 = rs . 1 , 22,000 answer : c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1320", "1300", "1325", "120" ] }
[ "C" ]
the present worth of rs . 1404 due in two equal half - yearly instalments at 8 % per annum . simple interest is :
"explanation : required sum = pw of rs . 702 due 6 months hence + pw of rs . 702 due 1 year hence = rs . [ 100 Γ— 702 / 100 + ( 8 Γ— 12 ) + 100 Γ— 702 / 100 + ( 8 Γ— 1 ) ] = rs . 1325 answer : c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "12.5 %", "20 %", "25 %", "50 %" ] }
[ "C" ]
ritesh and co . generated revenue of rs . 1,250 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 . 1,250 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1250 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) Γ— 1250 . = > 10,000 . hence , the total revenue by end of 2007 is rs . 10,000 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 10000 ) Γ— 100 . = > 25 % . answer : c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 500", "rs . 5100", "rs . 530", "rs . 540" ] }
[ "A" ]
find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 580 ?
"explanation : 580 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 500 answer : option a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "6", "14", "36", "21" ] }
[ "C" ]
√ ( 36 ) ^ 2
explanation √ ( 36 ) ^ 2 = ? or , ? = 36 answer c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "0.003", "0.0005", "0.25", "0.005" ] }
[ "D" ]
double of quarter of 1 percent written as a decimal is :
"explanation : solution : ( 2 ) * ( 1 / 4 ) * 1 % = 2 * ( 1 / 4 * 1 / 100 ) = 1 / 400 = 2 * 0.0025 = 0.005 . answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "350", "370", "380", "430" ] }
[ "C" ]
average expenditure of a person for the first 3 days of a week is rs . 340 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
"explanation : assumed mean = rs . 340 total excess than assumed mean = 4 Γ— ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 340 + rs . 40 = rs . 380 correct option : c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "10", "15", "20", "25" ] }
[ "B" ]
if 15 men , working 9 hours a day , can reap a field in 16 days , in how many days will 18 men reap the field , working 8 hours a day ?
let the required number of days be x . more men , less days ( indirect proportion ) less hours per day , more days ( indirect proportion ) men 18 : 15 hours per day 8 : 9 } : : 16 : x ( 18 x 8 x x ) = ( 15 x 9 x 16 ) = x = ( 44 x 15 ) 144 = 15 hence , required number of days = 15 . answer is b .
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs 14000", "rs 15000", "rs 16000", "rs 18000" ] }
[ "D" ]
a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 6480 interest . the principal amount borrowed by him was .
"explanation : s . i . = p Γ’ Λ† β€” r Γ’ Λ† β€” t / 100 = > p = s . i . Γ’ Λ† β€” 100 / r Γ’ Λ† β€” t = > p = 6480 Γ’ Λ† β€” 100 / 12 Γ’ Λ† β€” 3 = rs 18000 option d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "7450", "14900", "5625", "7500" ] }
[ "C" ]
vijay sells a cupboard at 16 % below cost price . had he got rs . 1800 more , he would have made a profit of 16 % . what is the cost price of the cupboard ?
explanation : cost price = 1800 / ( 0.16 + 0.16 ) = 1800 / 0.32 = rs . 5625 answer c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "7 h", "10 h", "8 h", "6 h" ] }
[ "A" ]
the area of a square field is 1225 km 2 . how long will it take for a horse to run around at the speed of 20 km / h ?
explanation area of field = 1225 km 2 . then , each side of field = √ 1225 = 35 km distance covered by the horse = perimeter of square field = 35 Γ— 4 = 140 km ∴ time taken by horse = distances / peed = 140 / 20 = 7 h answer a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "20", "11", "21", "41" ] }
[ "C" ]
the sum of the squares of 3 numbers is 241 , while the sum of their products taken two at a time is 100 . their sum is :
x ^ + y ^ 2 + z ^ 2 = 241 xy + yz + zx = 100 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 241 + ( 2 * 100 ) ( x + y + z ) ^ 2 = 441 so x + y + z = 21 answer : c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "7450", "14900", "6250", "6000" ] }
[ "C" ]
vijay sells a cupboard at 12 % below cost price . had he got rs . 1500 more , he would have made a profit of 12 % . what is the cost price of the cupboard ?
"explanation : cost price = 1500 / ( 0.12 + 0.12 ) = 1500 / 0.24 = rs . 6250 answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "35.2", "36.1", "30.5", "39.1" ] }
[ "C" ]
the mean of 50 observations was 30 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
"sol . therefore correct sum = ( 30 Γ— 50 + 48 – 23 ) = 1525 . therefore correct mean = 1525 / 50 = 30.5 . answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 169.50", "rs . 1700", "rs . 175.50", "rs . 155.50" ] }
[ "D" ]
tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 133 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 - 133 / 22.50 = 1 = Γ’ € ΒΊ x - 133 = 22.50 = Γ’ € ΒΊ x = 155.50 . hence , price of the third variety = rs . 155.50 per kg . answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "7500", "6500", "8875", "9500" ] }
[ "C" ]
find the simple interest on rs . 71,000 at 16 2 / 3 % per year for 9 months .
"p = rs . 71000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 71,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8875 answer is c ."
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "10", "6", "4", "0" ] }
[ "B" ]
a is a positive integer and multiple of 2 ; p = 4 ^ a , what is the remainder when p is divided by 10 ?
it is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer . to help see this , consider the following examples : 4 / 10 is 0 with a remainder of 4 14 / 10 is 1 with a remainder of 4 5 / 10 is 0 with a remainder of 5 105 / 10 is 10 with a remainder of 5 it is also essential to remember that the a is a positive integer and multiple of 2 . any integer that is a multiple of 2 is an even number . so , a must be a positive even integer . with these two observations , the question can be simplified to : what is the units digit of 4 raised to an even positive integer ? the units digit of 4 raised to an integer follows a specific repeating pattern : 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ ( odd number ) - - > units digit of 4 4 ^ ( even number ) - - > units digit of 6 there is a clear pattern regarding the units digit . 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6 . since a must be an even integer , the units digit of p = 4 ^ a will always be 6 . consequently , the remainder when p = 4 ^ a is divided by 10 will always be 6 . in case this is too theoretical , consider the following examples : a = 2 - - > p = 4 ^ a = 16 - - > p / 10 = 1 with a remainder of 6 a = 4 - - > p = 4 ^ a = 256 - - > p / 10 = 25 with a remainder of 6 a = 6 - - > p = 4 ^ a = 4096 - - > p / 10 = 409 with a remainder of 6 a = 8 - - > p = 4 ^ a = 65536 - - > p / 10 = 6553 with a remainder of 6 answer : b .
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "50 / 49", "1 / 289", "290 / 90", "290 / 19" ] }
[ "A" ]
product of two natural numbers is 7 . then , the sum of reciprocals of their squares is
"explanation : if the numbers are a , b , then ab = 7 , as 17 is a prime number , so a = 1 , b = 7 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 7 ( 2 ) = 50 / 49 option a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 72", "rs . 150", "rs . 112.50", "rs . 116.50" ] }
[ "B" ]
a 12 % stock yields 8 % . the market value of the stock is :
"solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 12 , investment = rs . ( 100 / 8 x 12 ) = rs . 150 ∴ market value of rs . 100 stock = rs . 150 answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1000", "800", "1400", "1200" ] }
[ "A" ]
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 . 5500 . what is the share of b ?
"let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ 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 . ( 5500 x ( 2 / 11 ) ) = rs . 1000 . answer is a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "15", "18", "16", "22" ] }
[ "C" ]
find the average of all the numbers between 11 and 21 which are divisible by 2 .
"sol . average = ( 12 + 14 + 16 + 18 + 20 / 5 ) = 80 / 5 = 16 . answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 25000", "rs . 20000", "rs . 15000", "rs . 22000" ] }
[ "B" ]
a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 400 . find the total worth of the stock ?
let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 400 = > x = 20000 answer : b
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 473", "rs . 374", "rs . 495", "rs . 630" ] }
[ "D" ]
compound interest of rs . 4000 at 10 % per annum for 1 1 / 2 years will be ( interest compounded half yearly ) .
10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 4000 [ 1 + ( 5 / 100 ) ] ^ 3 - 4000 = 4000 [ ( 21 / 20 ) ^ 3 - 1 ] = 4000 ( 9261 - 8000 ) / 8000 = 4 * 1261 / 8 = 630 answer : d
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "22000", "20000", "25123", "17272" ] }
[ "D" ]
sheela deposits rs . 3800 in bank savings account . if this is 22 % of her monthly income . what is her monthly income in ?
"explanation : 22 % of income = rs . 3800 100 % of income = 3800 x 100 / 22 = rs . 17272 answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "350", "370", "390", "430" ] }
[ "A" ]
average expenditure of a person for the first 3 days of a week is rs . 310 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
"explanation : assumed mean = rs . 310 total excess than assumed mean = 4 Γ— ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 310 + rs . 40 = rs . 350 correct option : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1200", "600", "750", "900" ] }
[ "D" ]
two equal sums of money were invested , one at 4 % and the other at 4.5 % . at the end of 7 years , the simple interest received from the latter exceeded to that received from the former by 31.50 . each sum was :
difference of s . i . = √ 31.50 let each sum be x . then x Γ— 4 1 / 2 Γ— 7 / 100 βˆ’ x Γ— 4 Γ— 7 / 100 = 31.50 or 7 ⁄ 100 x Γ— 1 ⁄ 2 = 63 ⁄ 2 or x = 900 answer d
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "52 kmph .", "62 kmph .", "97 kmph .", "80 kmph ." ] }
[ "C" ]
a man sitting in a train which is travelling at 15 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 - 15 ) kmph = 97 kmph . answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "150 %", "120 %", "130 %", "200 %" ] }
[ "A" ]
if the cost price is 40 % of selling price . then what is the profit percent .
"explanation : let the s . p = 100 then c . p . = 40 profit = 60 profit % = ( 60 / 40 ) * 100 = 150 % . answer : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "5", "14", "25", "21" ] }
[ "C" ]
√ ( 25 ) ^ 2
"explanation √ ( 25 ) ^ 2 = ? or , ? = 25 answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "16", "32", "64", "96" ] }
[ "D" ]
a and b can do a piece of work in 10 days , while b and c can do the same work in 15 days and c and a in 25 days . they started working together , after 4 days a left . after another 4 days b left . in how many days c can finish the remaining work ?
"let the rates of a , b and c be a , b , and c respectively . a and b can do a piece of work in 10 days : a + b = 1 / 10 ; b and c can do the same work in 15 days : b + c = 1 / 15 ; c and a can do the same work in 25 days : c + a = 1 / 25 . sum the above 3 equations : 2 ( a + b + c ) = 31 / 150 - - > a + b + c = 31 / 300 subtract a + b = 1 / 10 from above to get c = 1 / 300 . for 4 days all 3 worked and completed 4 * ( a + b + a ) = 124 / 300 of the work . for the next 4 days b and c worked and they completed 4 ( b + c ) = 4 / 15 = 80 / 300 of the work . so , by the time c is left alone 1 - ( 124 / 300 + 80 / 300 ) = 96 / 300 of the work is left to be completed by c alone . time = job / rate = ( 96 / 300 ) / ( 1 / 300 ) = 96 days . answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "195,143", "185,133", "175,123", "165,113" ] }
[ "A" ]
two numbers are in the ratio of 15 : 11 . if their h . c . f . is 13 , find the numbers .
let the required numbers be 15 . x and llx . then , their h . c . f . is x . so , x = 13 . the numbers are ( 15 x 13 and 11 x 13 ) i . e . , 195 and 143 . answer is a .
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4955", "4899", "4650", "7200" ] }
[ "A" ]
how many bricks each measuring 21 cm x 10 cm x 8 cm , will be needed to build a wall 9 m x 5 m x 18.5 m
"explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 900 x 500 x 18.5 ) / ( 21 x 10 x 8 ) = 4955 answer : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "$ 150", "$ 900", "$ 600", "$ 450" ] }
[ "B" ]
profits in the partnership of bess , bill and bob are shared in the ratio 1 : 2 : 3 . if bill ' s share of the profits is $ 300 , what is bob ' s share ?
ans is d given profit ratio , bess : bill : bob = 1 : 2 : 3 to make bill ' s portion $ 300 , multiply by $ 150 = > bess : bill : bob = $ 150 : $ 300 : $ 450 = > bob ' s share = $ 450
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "15 %", "20 %", "25 %", "30 %" ] }
[ "B" ]
if the price of sugar rises from rs . 6 per kg to rs . 7.50 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
"sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 6 = x Γ— 7.50 = x = 80 kg . ∴ reduction in consumption = 20 % . answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "144 mins", "140 mins", "136 mins", "156 minw" ] }
[ "D" ]
one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 39 minutes , then the slower pipe alone will be able to fill the tank in
"explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 39 = > 4 / x = 1 / 39 x = 39 βˆ— 4 = 156 mins option d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "79698", "20578", "80698", "81268" ] }
[ "B" ]
117 x 217 + 83 x 83 = ?
"= ( 117 ) ^ 2 + ( 83 ) ^ 2 = ( 100 + 17 ) ^ 2 + ( 100 - 17 ) ^ 2 = 2 [ ( 100 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 10000 + 289 ] = 2 x 10289 = 20578 answer is b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1948816", "1981709", "18362619", "2031719" ] }
[ "A" ]
1396 x 1396
"1396 x 1396 = ( 1396 ) 2 = ( 1400 - 2 ) 2 = ( 1400 ) 2 + ( 4 ) 2 - ( 4 x 1400 x 4 ) = 1948816 . answer : option a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2', '", "4', '", "8', '", "16', '" ] }
[ "C" ]
in the rectangular coordinate system , points ( 8 , 0 ) and ( – 8 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
the answer is c 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 isgreater 8 c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "40", "60", "64", "72" ] }
[ "C" ]
a typist uses a sheet measuring 20 cm by 30 cm lengthwise . if a margin of 2 cm is left on each side and a 3 cm margin on top and bottom , then percent of the page used for typing is
solution area of the sheet = ( 20 x 30 ) cm Β² = 600 cm Β² area used for typing = [ ( 20 - 4 ) x ( 30 - 6 ) ] cm Β² = 384 cm Β² required percentage = ( 384 / 600 x 100 ) % = 64 % . answer c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "66 , 78", "70 , 82", "94 , 106", "84 , 96" ] }
[ "D" ]
the h . c . f . of two numbers is 12 and their difference is 12 . the numbers are :
explanation : out of the given numbers , the two with h . c . f . 12 and difference 12 are 84 and 96 . answer is d
MathQA
{ "label": [ "B", "C", "D", "E" ], "text": [ "3", "4", "1", "5" ] }
[ "E" ]
calculate how long it will take a swimmer to swim a distance of 8 km against the current of a river which flows at 1.4 km / hr , given that he can swim in still water at 3 km / h
swim in still water at = 3 speed of river = 1.4 us = 3 - 1.4 = 1.6 distance = 8 t = 8 / 1.6 = 5 answer : e
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1200", "160", "360", "240" ] }
[ "B" ]
average age of students of an adult school is 48 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
explanation : let the original no . of students be x . according to situation , 48 x + 120 * 32 = ( x + 120 ) 36 β‡’ x = 40 so , required no . of students after joining the new students = x + 120 = 160 . answer : b
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "3 hours", "2.4 hours", "1.4 hours", "1 hour" ] }
[ "D" ]
in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . what is the duration of the flight ?
"explanation : let the duration of the flight be x hours . then 600 / x βˆ’ 600 / x + 1 / 2 = 200 600 / x βˆ’ 1200 / 2 x + 1 = 200 x ( 2 x + 1 ) = 3 2 x 2 + x βˆ’ 3 = 0 = > ( 2 x + 3 ) ( x βˆ’ 1 ) = 0 neglecting the negative value for x we get x = 1 option d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "150 m", "200 m", "125 m", "115 m" ] }
[ "A" ]
a tree is 12 m tall and casts an an 8 m long shadow . at the same time , a flag pole caste a 100 m long shadow . how long is the flag pole ?
answer ∡ 8 m shadow means original height = 12 m ∴ 1 m shadow means original height = 12 / 8 m ∴ 100 m shadow means original height = ( 12 / 8 ) x 100 m = ( 6 / 4 ) x 100 = 6 x 25 = 150 m correct option : a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "28 %", "25 %", "18.5 %", "16 %" ] }
[ "A" ]
a company charges a fixed rental of rs . 350 per month . it allows 200 calls free per month . each call is charge at rs . 1.4 when the number of calls exceed 200 per month and it charges rs . 1.6 when the number of calls exceeds 400 per month and so on . a customer made 150 calls in february and 250 calls in march . by how much percent each call is cheaper in march than each call in february .
solution : charge per call in february = 350 / 150 = 7 / 3 = 2.33 charge per call in march = [ 350 + ( 50 * 1.4 ) ] / 250 = 420 / 250 = 42 / 25 = 1.68 % cheaper call rate in march = [ ( 2.33 - 1.68 ) / 2.33 ] * 100 = 28 % . answer : option a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "151", "149", "152", "148" ] }
[ "A" ]
the mean of 30 values was 150 . it was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean . find the correct mean .
"corrected mean = 150 Γ— 30 βˆ’ 135 + 165 / 30 = 4500 βˆ’ 135 + 165 / 30 = 4530 / 30 = 151 answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "725", "720", "600", "525" ] }
[ "D" ]
25 x 10 + 25 x 11 = ?
"= 25 x ( 10 + 11 ) ( by distributive law ) = 25 x 21 = 525 answer is d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1 / 20", "1 / 50", "1 / 75", "1 / 25" ] }
[ "A" ]
what will be the fraction of 5 %
"explanation : 5 * 1 / 100 = 1 / 20 . option a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "160", "180", "200", "220" ] }
[ "A" ]
a number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ?
"answer let the number be n . then , ( n / 5 ) + 4 = ( n / 4 ) - 4 Γ’ ‑ ’ ( n / 4 ) - ( n / 5 ) = 8 Γ’ ‑ ’ ( 5 n - 4 n ) / 20 = 8 Γ’ Λ† Β΄ n = 160 option : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "75142", "64851", "5149", "69993" ] }
[ "D" ]
the difference between the local value and the face value of 7 in the numerical 32675149 is
"= ( local value of 7 ) - ( face value of 7 ) = ( 70000 - 7 ) = 69993 answer is d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "0.64202", "0.64204", "0.642022", "0.642075" ] }
[ "D" ]
the average of numbers 0.64206 , 0.64207 , 0.64208 and 0.64209 is ?
"answer average = ( 0.64206 + 0.64207 + 0.64208 + 0.64209 ) / 4 = 2.5683 / 4 = 0.642075 correct option : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "13000", "7000", "10000", "4375" ] }
[ "D" ]
a textile manufacturing firm employees 80 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 80 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 Γ’ Λ† ’ ( 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 Γ£ β€” ( 79 / 80 ) Γ’ Λ† ’ 150000 Γ£ β€” ( 79 / 80 ) Γ’ Λ† ’ 75000 . = > rs 2 , 70,625 . decrease in profit = > 2 , 75,000 Γ’ Λ† ’ 2 , 70,625 = > rs . 4,375 answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "20 %", "25 %", "33.33 %", "35 %" ] }
[ "D" ]
a milk man has 30 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 30 liters of milk . therefore , profit percentage = 35 % . answer : d
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "89 %", "97.1 %", "96.1 %", "86.1 %" ] }
[ "C" ]
in a factory there are 3 types of machine m 1 , m 2 and m which produces 25 % , 35 % and 40 % of the total products respectively . m 1 , m 2 and m 3 produces 2 % , 4 % and 5 % defective products , respectively . what is the percentage of non - defective products ?
solution : non - defective products , { [ ( 25 * 0.98 ) + ( 35 * 0.96 ) + ( 40 * 0.95 ) ] / 100 } * 100 = 96.1 % . answer : option c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "230 m", "350 m", "260 m", "270 m" ] }
[ "B" ]
a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 30 seconds . what is the length of the goods train ?
"explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 30 sec . let the length of the train be x metres . then , [ ( x + 250 ) / 30 ] = 20 = > x + 250 = 600 = > x = 350 . answer : b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "10 %", "50 %", "25 %", "52 %" ] }
[ "C" ]
a retailer buys a radio for rs 225 . his overhead expenses are rs 15 . he sellis the radio for rs 300 . the profit percent of the retailer is
"explanation : cost price = ( 225 + 15 ) = 240 sell price = 300 gain = ( 60 / 240 ) * 100 = 25 % . answer : c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "6 %", "8 %", "9 %", "10 %" ] }
[ "B" ]
the simple interest on a certain sum of money at the rate of 5 % p . a . for 8 years is rs . 840 . at what rate of interest the same amount of interest can be received on the same sum after 5 years ?
"solution s . i . = rs . 840 , r = 5 % , t = 8 years . principal = rs . ( 800 x 840 / 5 x 8 ) = rs . 2100 . now , p = rs . 2100 , s . i . = rs . 840 , t = 5 years . ∴ rate = ( 100 x 840 / 2100 x 5 ) = 8 % . answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 340", "rs . 840", "rs . 1020", "rs . 760" ] }
[ "A" ]
the banker Γ’ € β„’ s gain on a sum due 3 years hence at 12 % per annum is rs . 90 . the banker Γ’ € β„’ s discount is
"solution t . d = ( b . g x 100 / r x t ) = rs . ( 90 x 100 / 12 x 3 ) = rs . 250 . b . d = rs ( 250 + 90 ) = rs . 340 . answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "$ 50", "$ 64", "$ 75", "$ 96" ] }
[ "A" ]
if greg buys 3 shirts , 4 trousers and 2 ties , the total cost is $ 40 . if greg buys 7 shirts , 2 trousers and 2 ties , the total cost is $ 60 . how much will it cost him to buy 3 trousers , 5 shirts and 2 ties ?
"solution : 3 x + 4 y + 2 z = 40 7 x + 2 y + 2 z = 60 adding both the equations = 10 x + 6 y + 4 z = 100 5 x + 3 y + 2 z = 50 ans a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs 800", "rs 820", "rs 860", "rs 850" ] }
[ "D" ]
the sale price of a trolley bag including the sale tax is rs . 1190 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :
"explanation : 112 % of s . p . = 1190 s . p . = rs . ( 1190 x 100 / 112 ) = rs . 1062.50 . c . p . = rs ( 100 / 125 x 1062.50 ) = rs 850 answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "75 m .", "80 m .", "150 m .", "100 m ." ] }
[ "D" ]
a runs twice as fast as b and gives b a start of 50 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 50 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 50 m is 50 / 1 = 50 m so the total time taken by a and b to reach = 2 * 50 = 100 m answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "7000", "8000", "9261", "9999" ] }
[ "C" ]
the largest four digit number which is a perfect cube , is :
"explanation : 21 * 21 * 21 = 9261 option c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 1000", "rs . 1550", "rs . 1510", "rs . 1500" ] }
[ "D" ]
find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 1740 ?
"explanation : 1740 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1500 answer : option d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "196", "158", "192", "200" ] }
[ "C" ]
how many digits are required to write numbers between 1 to 100 .
"explanation : single digits are from 1 to 9 = 9 digits doubt digits are from 10 to 99 = 90 x 2 = 180 digits 100 needs 3 digits . total 192 digits correct option : c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "21", "24", "27", "36" ] }
[ "C" ]
the sum of three consecutive even numbers multiples of 3 is 72 . what is the largest number ?
"solution let the number be x and x + 2 . then , ( x + 2 ) 2 - x 2 = 84 ⇔ 4 x + 4 = 84 ⇔ 4 x = 80 ⇔ x = 20 . ∴ required sum = x + ( x + 2 ) = 2 x + 2 = 42 . answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "156", "220", "130", "240" ] }
[ "B" ]
6 friends went to a hotel and decided to pay the bill amount equally . but 5 of them could pay rs . 100 each as a result 6 th has to pay rs . 100 extra than his share . find the amount paid by him .
"explanation : average amount paid by 5 persons = rs . 100 increase in average due to rs . 120 paid extra by the 6 th men = rs . 100 / 5 = rs . 20 therefore , average expenditure of 6 friends = rs . 100 + rs . 20 = rs . 120 therefore , amount paid by the 6 th men = rs . 120 + rs . 100 = rs . 220 correct option : b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "120", "100", "75", "90" ] }
[ "A" ]
if 50 % of 3 / 5 of a number is 36 , then the number is ?
let the number be x . then 50 % of 3 / 5 of x = 36 50 / 100 * 3 / 5 * x = 36 x = ( 36 * 10 / 3 ) = 120 required number = 120 . correct option : a
MathQA
{ "label": [ "A", "B", "C", "E" ], "text": [ "1000", "1030", "1100", "1101" ] }
[ "A" ]
what annual installment will discharge a debt of rs . 4600 due in 4 years at 10 % simple interest ?
"let the 1 st installment = 100 / - it is 3 yrs before due iind is 2 yr before due iii 3 rd is 1 yr before due ivth is 0 yrs before due on 1 st installment interest will be paid for 3 yrs 2 nd installment interest will be paid for 2 yrs 3 rd installment interest will be paid for 1 yr 4 th installment interest will be paid for 0 yr interest = p [ ( 100 ( 3 + 2 + 1 + 0 ) x 10 ) / 100 ] = 60 / - total loan discharged = 4 * 100 + 60 / - = 460 / - now installment of 100 / - loan discharged = 460 / - loan discharged 4600 / - ? installment = 1000 / - answer : a ."
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 500", "rs . 840", "rs . 650", "rs . 720" ] }
[ "B" ]
a man invested rs . 14,400 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": [ "62.6 km", "26.7 km", "22.8 km", "19.5 km" ] }
[ "B" ]
a walks at 4 kmph and 4 hours after his start , b cycles after him at 10 kmph . how far from the start does b catch up with a ?
"sol . suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 4 hours . ∴ x / 4 - x / 10 = 4 or x = 26.7 km . answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "110", "111", "115", "123" ] }
[ "C" ]
11 friends went to a hotel and decided to pay the bill amount equally . but 10 of them could pay rs . 60 each as a result 11 th has to pay rs . 50 extra than his share . find the amount paid by him .
explanation : average amount paid by 10 persons = rs . 60 increase in average due to rs . 50 paid extra by the 11 th men = rs . 50 / 10 = rs . 5 therefore , average expenditure of 11 friends = rs . 60 + rs . 5 = rs . 65 therefore , amount paid by the 11 th men = rs . 65 + rs . 50 = rs . 115 correct option : c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "12 hours", "24 hours", "36 hours", "48 hours" ] }
[ "B" ]
speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph . a man rows to place at a distance of 105 km and comes back to the starting point . the total time taken by him is :
"sol . speed upstream = 7.5 kmph ; speed downstream = 10.5 kmph . ∴ total time taken = [ 105 / 7.5 + 105 / 10.5 ] hours = 24 hours . answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "19 %", "10 %", "22 %", "16 %" ] }
[ "C" ]
weights of two friends ram and shyam are in the ratio 7 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
"solution : given ratio of ram and shayam ' s weight = 7 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 7 / 5 or , x = 22 % . answer : option c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "10.2 kmph", "10.4 kmph", "10.8 kmph", "11.8 kmph" ] }
[ "C" ]
a boy rides his bicycle 10 km at an average sped of 12 km / hr and again travels 12 km at an average speed of 10 km / hr . his average speed for the entire trip is approximately .
sol . total distance travelled = ( 10 + 12 ) km / hr = 22 km / hr . total time taken = [ 10 / 12 + 12 / 10 ] hrs = 61 / 30 hrs ∴ average speed = [ 22 * 30 / 61 ] km / hr = 10.8 km / hr . answer c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2400", "2000", "1904", "1906" ] }
[ "A" ]
106 x 106 - 94 x 94 = ?
"= ( 106 ) ^ 2 - ( 94 ) ^ 2 = ( 106 + 94 ) ( 106 - 94 ) = ( 200 x 12 ) = 2400 answer is a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "85", "94", "83", "72" ] }
[ "C" ]
the sum of digits of a two digit number is 11 , the difference between the digits is 5 . find the number
"description : = > x + y = 11 , x - y = 5 adding these 2 x = 16 = > x = 8 , y = 3 . thus the number is 83 answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "0", "0", "27", "54" ] }
[ "B" ]
for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.267 ] = 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 . b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "8925", "8032.5", "7302.3", "8900" ] }
[ "C" ]
a sum fetched total simple interest of 4016.25 at the rate of 11 p . c . p . a . in 5 years . what is the sum ?
"let the sums be p . now , 55 % of p = 4016.25 or , p = 7302.3 answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "58 kg", "60 kg", "64 kg", "70 kg" ] }
[ "B" ]
zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 27 kg of zinc has been consumed in it ?
"sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 27 kg zinc , mixture , melted = [ 20 / 9 x 27 ] kg = 60 kg . answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "0.03", "0.0005", "0.25", "0.005" ] }
[ "A" ]
double of quarter of 6 percent written as a decimal is :
"explanation : solution : ( 2 ) * ( 1 / 4 ) * 6 % = 0.03 answer : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "350", "370", "390", "400" ] }
[ "D" ]
average expenditure of a person for the first 3 days of a week is rs . 360 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
"explanation : assumed mean = rs . 360 total excess than assumed mean = 4 Γ— ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 360 + rs . 40 = rs . 400 correct option : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "7 / 19", "6 / 19", "5 / 19", "4 / 19" ] }
[ "A" ]
a box contains 20 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
"explanation : please remember that maximum portability is 1 . so we can get total probability of non defective bulbs and subtract it form 1 to get total probability of defective bulbs . so here we go , total cases of non defective bulbs 16 c 2 = 16 βˆ— 15 / 2 βˆ— 1 = 120 total cases = 20 c 2 = 20 βˆ— 19 / 2 βˆ— 1 = 190 probability = 120 / 190 = 12 / 19 p of at least one defective = 1 βˆ’ 12 / 19 = 7 / 19 option a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "10.22 %", "20.22 %", "21.22 %", "43.75 %" ] }
[ "D" ]
a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 15 % while buying and by 20 % while selling . what is his percentage profit ?
"the owner buys 100 kg but actually gets 115 kg ; the owner sells 100 kg but actually gives 80 kg ; profit : ( 115 - 80 ) / 80 * 100 = ~ 43.75 % answer : d ."
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs 10123.20", "rs 12147.84", "rs 10123.40", "rs 10123.50" ] }
[ "B" ]
what will be the compound interest on rs . 30000 after 3 years at the rate of 12 % per annum
"explanation : ( 30000 Γ— ( 1 + 12 / 100 ) 3 ) = > 30000 Γ— 28 / 25 Γ— 28 / 25 Γ— 28 / 25 = > 42147.84 so compound interest will be 42147.84 - 30000 = rs 12147.84 option b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "200 m", "400 m", "500 m", "700 m" ] }
[ "C" ]
a train speeds past a pole in 20 seconds and passes through a tunnel 500 m long in 40 seconds . its length is :
sol . let the length of the train be x metres and its speed be y m / sec . then , x / y = 20 β‡’ y = x / 20 ∴ ( x + 500 ) / 40 = x / 20 ⇔ x = 500 m . answer c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1 / 4", "1 / 6", "1 / 7", "3 / 4" ] }
[ "D" ]
a can finish a work in 4 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?
explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 4 b ' s 1 day work = 1 / 2 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 4 + 1 / 2 ) = 3 / 4 so in one day 3 / 4 work will be done answer : d
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "9,6", "11,5", "9,3", "6,6" ] }
[ "B" ]
a man can row downstream at the rate of 16 km / hr and upstream at 6 km / hr . find man ' s rate in still water and the rate of current ?
"explanation : rate of still water = 1 / 2 ( 16 + 6 ) = 11 km / hr rate of current = 1 / 2 ( 16 - 6 ) = 5 km / hr answer : option b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1314", "1312", "1334", "1344" ] }
[ "C" ]
a alone can complete a work in 16 days and b alone can do in 12 days . star Ι΅ ng with a , they work on alternate days . the total work will be completed in
explana Ι΅ on : a ' s 1 day work = 1 / 16 b ' s 1 day work = 1 / 12 as they are working on alternate day ' s so their 2 days work = ( 1 / 16 ) + ( 1 / 12 ) = 7 / 48 [ here is a small technique , total work done will be 1 , right , then mul Ι΅ ply numerator Ι΅ ll denominator , as 7 * 6 = 42 , 7 * 7 = 49 , as 7 * 7 is more than 48 , so we will consider 7 * 6 , means 6 pairs ] work done in 6 pairs = 6 * ( 7 / 48 ) = 7 / 8 remaining work = 1 - 7 / 8 = 1 / 8 on 13 th day it will a turn , then remaining work = ( 1 / 8 ) - ( 1 / 16 ) = 1 / 16 on 14 th day it is b turn , 1 / 12 work done by b in 1 day 1 / 16 work will be done in ( 12 * 1 / 16 ) = 3 / 4 day so total days = 1334 answer : c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "51 : 52", "52 : 53", "53 : 54", "54 : 53" ] }
[ "D" ]
the cash difference between the selling prices of an article at a profit of 8 % and 6 % is rs 3 . the ratio of two selling prices is
"explanation : let the cost price of article is rs . x required ratio = ( 108 % of x ) / ( 106 % of x ) = 108 / 106 = 54 / 53 = 54 : 53 . answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "90", "60", "30", "1911" ] }
[ "C" ]
the maximum number of student amoung them 2010 pens and 1050 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 2010 and 1050 = 30 . answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "55.22 %", "54.54 %", "63 %", "70 %" ] }
[ "A" ]
a cricketer scored 134 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
"explanation : number of runs made by running = 134 - ( 12 x 4 + 2 x 6 ) = 134 - ( 60 ) = 74 now , we need to calculate 72 is what percent of 134 . = > 74 / 134 * 100 = 55.22 % answer : a"
MathQA