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MNLP_M3_mathqa

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{ "label": [ "B", "C", "D", "E" ], "text": [ "4", "5", "8", "9" ] }
[ "C" ]
how many points ( x , y ) lie on the line segment between ( 32 , 12 2 / 3 ) and ( 7 , 17 2 / 3 ) such that x and y are both integers ?
"slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 7 - 32 ) = - 1 / 5 y = mx + b = > 12 2 / 3 = - 22 / 3 + b = > b = 19 y = - x / 5 + 19 only integer values work , and the only multiples of 5 between 7 and 32 for x values are 10 , 15 , 20 , 25 and 30 , thus 5 points . c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "0.46", "0.56", "0.64", "0.65" ] }
[ "A" ]
solve : 0.6 * 0.6 + 0.6 * 0.6
"= 0.6 * 0.6 + ( 0.6 * 6 ) = 0.36 + 0.1 = 0.46 answer is a ."
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "40 m 2', '", "44 m 2', '", "48 m 2', '", "37.7 m 2', '" ] }
[ "D" ]
the diameter of a garden roller is 1.2 m and it is 2 m long . how much area will it cover in 5 revolutions ? ( use Γ― € = 22 Γ’  β€ž 7 )
required area covered in 5 revolutions = 5 Γ£ β€” 2 Γ― € rh = 5 Γ£ β€” 2 Γ£ β€” 22 Γ’  β€ž 7 Γ£ β€” 0.6 Γ£ β€” 2 = 37.7 m 2 answer d
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "3.84', '", "1.75', '", "3.36', '", "2.72', '" ] }
[ "C" ]
the weights of one liter vegetable ghee packet of two brands β€˜ a ’ and β€˜ b ’ are 900 gm and 750 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?
here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . eachpartis 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4", "5", "6", "10" ] }
[ "D" ]
suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 25 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?
"the part of job that suresh completes in 9 hours = 9 Γ’  β€ž 15 = 3 Γ’  β€ž 5 remaining job = 1 - 3 Γ’  β€ž 5 = 2 Γ’  β€ž 5 remaining job can be done by ashutosh in 2 Γ’  β€ž 5 Γ£ β€” 25 = 10 hours answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "18.94 %", "18.93 %", "18.92 %", "18.91 %" ] }
[ "B" ]
a shopkeeper fixes the marked price of an item 32 % above its cost price . the percentage of discount allowed to gain 7 % is
"explanation : let the cost price = rs 100 then , marked price = rs 132 required gain = 7 % , so selling price = rs 107 discount = 132 - 107 = 25 discount % = ( 25 / 132 ) * 100 = 18.93 % option b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2", "4", "8", "16" ] }
[ "B" ]
in the rectangular coordinate system , points ( 5 , 0 ) and ( – 5 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
"the answer is b 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": [ "B", "C", "D", "E" ], "text": [ "12 p . m .", "3 pm .", "2 p . m .", "1 p . m ." ] }
[ "D" ]
the distance between 2 cities a and b is 1000 km . a train starts from a at 9 a . m . and travels towards b at 100 km / hr . another starts from b at 10 a . m . and travels towards a at 150 km / hr . at what time do they meet ?
"suppose they meet x hrs after 9 a . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 9 + 5 = 2 p . m . answer is d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "31", "56", "41", "59" ] }
[ "D" ]
the average age of 42 students in a group is 16 years . when teacher Γ’ € β„’ s age is included to it , the average increases by one . what is the teacher Γ’ € β„’ s age in years ?
"sol . age of the teacher = ( 43 Γ£ β€” 17 Γ’ € β€œ 42 Γ£ β€” 16 ) years = 59 years . answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "80 m", "180 m", "100 m", "60 m" ] }
[ "A" ]
the length of 3 ropes are in the ratio 4 : 5 : 6 . if the sum of the weights of the longest and the shortest rope is 100 metres more than the length of the third rope , what is the length of the shortest rope ?
let the lengths of the three ropes be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 100 = > 5 k = 100 = > k = 20 therefore the weight of the lightest boy = 4 k = 4 ( 20 ) = 80 m answer : a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "6.12 hr", "8 hr", "8.5 hr", "10 hr" ] }
[ "A" ]
two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 50 hr . if all pipes are opened simultaneously , then the cistern will be filled in
solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 βˆ’ 1 / 50 = 8 / 49 hence , tank will be filled in 49 / 8 = 6.12 hour option ( a )
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1 kg", "10.8 kg", "11 kg", "14.9 kg" ] }
[ "A" ]
the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.2 kg . the weight of the new student is ?
"answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.2 - 19 x 15 ) kg = 1 kg . correct option : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "12 kg", "60 kg", "72 kg", "96 kg" ] }
[ "B" ]
a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of man is
"solution volume of water displaced = ( 3 x 2 x 0.01 ) m 3 = 0.06 m 3 . mass of man = volume of water displaced Γ— density of water = ( 0.06 Γ— 1000 ) kg = 60 kg . answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "10 hours", "12 hours", "14 hours", "16 hours" ] }
[ "B" ]
in a river flowing at 2 km / hr , a boat travels 32 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 = 32 km total time taken = time taken downstream + time taken upstream = ( 32 / 8 ) + ( 32 / 4 ) = ( 32 / 8 ) + ( 64 / 8 ) = ( 96 / 8 )...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1100", "800", "1400", "600" ] }
[ "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 . 3300 . 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 . ( 3300 x ( 2 / 11 ) ) = rs . 600 answer is d ."
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "277", "36", "64", "40" ] }
[ "D" ]
? % of 360 = 144
"? % of 360 = 144 or , ? = 144 Γ— 100 / 360 = 40 answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4,0", "0,4", "4,4", "0,0" ] }
[ "A" ]
which digits should come in place of @ and # if the number 62684 @ # is divisible by both 8 and 5 ?
explanation : since the given number is divisible by 5 , so 0 or 5 must come in place of # . but , a number ending with 5 is never divisible by 8 . so , 0 will replace # . now , the number formed by the last three digits is 4 @ 0 , which becomes divisible by 8 , if @ is replaced by 4 . hence , digits in place of @ and ...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 120", "rs . 210", "rs . 240", "rs . 300" ] }
[ "B" ]
a sum of rs . 1190 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 1190 = > 17 x / 12 = 1190 = > 1190 x 12 / 17 = rs . 840 hence , b ’ s share = rs . ( 840 / 4 ) = rs . 210 . answer b
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "10 %", "20 %", "30 %", "32 %" ] }
[ "B" ]
if the selling price of 10 articles is same as the cost price of 12 articles . find the gain or loss percentage ?
"let the c . p of each article be re 1 . then , s . p of 10 articles = c . p of 12 articles = rs . 12 now , c . p of 10 articles = rs . 10 , s . p of 10 articles = rs 12 gain = rs ( 12 - 10 ) = rs 2 . gain % = ( 2 / 10 Γ— 100 ) % = 20 % b )"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "9 m", "9.5 m", "10.5 m", "12 m" ] }
[ "B" ]
a ladder learning against a wall makes an angle of 60 Β° with the ground . if the length of the ladder is 19 m , find the distance of the foot of the ladder from the wall .
let ab be the wall and bc be the ladder . then , < abc = 60 Β° and , bc = 19 m . ; ac = x metres ac / bc = cos 60 Β° = x / 19 = 1 / 2 x = 19 / 2 = 9.5 m . answer b
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 75", "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 . 9 . the true discount is
"solution t . d = [ b . g x 100 / r x t ] = rs . ( 9 x 100 / 12 x 1 ) = rs . 75 . answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "152600 m 2", "153500 m 2", "153600 m 2", "153800 m 2" ] }
[ "C" ]
the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 minutes , then the area of the park ( in sq . m ) is :
"explanation : question seems to be typical , but trust me it is too easy to solve , before solving this , lets analyse how we can solve this . we are having speed and time so we can calculate the distance or perimeter in this question . then by applying the formula of perimeter of rectangle we can get value of length ...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "3 : 4", "3 : 5", "4 : 5", "6 : 5" ] }
[ "D" ]
a man invests some money partly in 4 % stock at 48 and partly in 10 % stock at 110 . 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 . ( 48 / 4 ) = rs . 12 . for an income of rs . 1 in 12 % stock at 120 , investment = rs . ( 110 / 10 ) = rs . 10 . ∴ ratio of investments = 12 : 10 = 6 : 5 answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "0.625", "0.0625", "6.25", "0.00625" ] }
[ "D" ]
what is 25 % of 25 % equal to
"solution 25 % of 25 % = 25 / 100 x 25 / 100 = 1 / 16 = 0.0625 answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "50 kmph", "60 kmph", "32 kmph", "70 kmph" ] }
[ "C" ]
a car takes 6 hours to cover a distance of 288 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
"time = 6 distence = 288 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 288 / 9 = 32 kmph c )"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "182", "176", "175", "96" ] }
[ "A" ]
a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 273 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 ( 273 + l ) / 20 = l / 8 2184 + 8 l = 20 l l = 2184 / 12 = 182 m answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1.2", "1.4", "6", "7" ] }
[ "C" ]
the simple interest on rs . 20 for 6 months at the rate of 5 paise per rupeeper month is
"sol . s . i . = rs . [ 20 * 5 / 100 * 6 ] = rs . 6 answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ ". 4 km", "1.4 km", "2.4 km", "3.4 km" ] }
[ "C" ]
a man can row at 5 kmph in still water . if the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back . how far is that place .
"explanation : let the distance is x km rate downstream = 5 + 1 = 6 kmph rate upstream = 5 - 1 = 4 kmph then x / 6 + x / 4 = 1 [ because distance / speed = time ] = > 2 x + 3 x = 12 = > x = 12 / 5 = 2.4 km option c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "100", "1000", "10000", "100000" ] }
[ "C" ]
it costs a publishing company 50000 dollars to make books . the 50000 is a fixed cost or a cost that can not change . to help the publishing company sell the books , a marketing company charges 4 dollars for each book sold . if the company charges 9 dollars per book , how many books should they sell to break even ?
let c be the cost of producing and selling x books let r be the revenue made for selling x books r = selling price of 1 book Γ— number of books sold r = 9 x c = fixed cost + variable cost variable cost = fee charged for 1 book Γ— number of books sold variable cost = 4 x c = 50000 + 4 x r = c 9 x = 50000 + 4 x 9 x - 4 x =...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "110.5", "111.5", "112.5", "113.5" ] }
[ "C" ]
sachin borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends money to rahul at 25 / 4 % p . a . for 2 years . find the gain of one year by sachin .
explanation : two things need to give attention in this question , first we need to calculate gain for 1 year only . gain in 2 year = [ ( 5000 Γ— 254 Γ— 2100 ) βˆ’ ( 5000 Γ— 4 Γ— 2100 ) ] = ( 625 βˆ’ 400 ) = 225 so gain for 1 year = 2252 = 112.50 answer : c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "40", "50", "90", "140" ] }
[ "A" ]
if the average ( arithmetic mean ) of a and b is 50 and the average of b and c is 70 , what is the value of c βˆ’ a ?
"- ( a + b = 100 ) b + c = 140 c - a = 40 a . 40"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2 : 3", "3 : 2", "1 : 3", "2 : 1" ] }
[ "B" ]
gold is 19 times as heavy as water and copper is 9 times heavy . in what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water ?
"? required ratio = 6 ? 4 = 3 : 2 answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "22 hours", "30 hours", "44 hours", "60 hours" ] }
[ "C" ]
together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours t would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( ass...
"say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above :...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "24 , 2", "12 , 6", "15 , 3", "14 , 4" ] }
[ "A" ]
a man can row downstream at 26 kmph and upstream at 22 kmph . find the speed of the man in still water and the speed of stream respectively ?
"explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 26 - - - ( 1 ) and x - y = 22 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 48 = > x = 24 , y = 2 . answer : option a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "3000", "6000", "2000", "4000" ] }
[ "B" ]
a sum was put at simple interest at a certain rate for 3 years . had it been put at 2 % higher rate , it would have fetched rs . 360 more . find the sum .
"let sum = p and original rate = r . then , [ ( p * ( r + 2 ) * 3 ) / 100 ] – [ ( p * r * 3 ) / 100 ] = 360 . = 3 pr + 6 p - 3 pr = 36000  6 p = 36000  p = 6000 hence , sum = rs . 6000 . answer is b ."
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "3327", "3237", "3337", "2337" ] }
[ "A" ]
9873 + x = 13200 , then x is ?
"answer x = 13200 - 9873 = 3327 option : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 4000", "rs . 665.6", "rs . 520", "rs . 166.4" ] }
[ "C" ]
simple interest on a certain sum of money for 2 years at 16 % per annum is one fourth the compound interest on rs . 4000 for 2 years at 8 % per annum . the sum placed on simple interest is
"solution c . i . = rs [ 4000 x ( 1 + 8 / 100 ) Γ’ Β² - 4000 ] rs . ( 4000 x 108 / 100 x 108 / 100 - 4000 ) = rs . 665.6 . sum = rs . [ 166.4 x 100 / 2 x 16 ] = rs . 520 . answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "6.06 %", "6.07 %", "6.08 %", "6.09 %" ] }
[ "D" ]
the effective annual rate of interest corresponding to a nominal rate of 6 % per annum payable half yearly is
"solution amount of rs . 100 for 1 year when compounded half yearly = rs . [ 100 x ( 1 + 3 / 100 ) 2 ] = rs . 106.09 % . effective rate = ( 106.09 - 100 ) % = rs . 6.09 % . answer d"
MathQA
{ "label": [ "B", "C", "D", "E" ], "text": [ "1 hour", "1 hour 15 min", "1 hour 30 min", "1 hour 10 min" ] }
[ "D" ]
a boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . how long will it take to go 6 km in stationary water ?
"speed ( upstream ) = 2 / 1 = 2 kmhr speed ( downstream ) = 1 / ( 10 / 60 ) = 6 kmhr speed in still water = 1 / 2 ( 2 + 6 ) = 4 kmhr time taken in stationary = 6 / 4 = 1 hrs 30 min answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2.29", "2.75", "4.25", "4.5" ] }
[ "B" ]
( 17 ) 5.25 x ( 17 ) ? = 178
"solution let ( 17 ) 5.25 * ( 17 ) x = 178 . then , ( 17 ) 5.25 + x = ( 17 ) 8 . ∴ 5.25 + x = 8 ⇔ x = ( 8 - 5.25 ) ⇔ x = 2.75 answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4 %", "5 %", "6 %", "8.75 %" ] }
[ "A" ]
the population of a town increased from 1 , 75,000 to 2 , 45,000 in a decade . the average percent increase of population per year is
"solution increase in 10 years = ( 245000 - 175000 ) = 87500 . increase % = ( 70000 / 175000 Γ£ β€” 100 ) % = 40 % . required average = ( 40 / 10 ) % = 4 % . answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1997", "1998", "1999", "2000" ] }
[ "B" ]
the price of commodity x increases by 40 paise every year , while the price of commodity y increases by 15 paise every year . if in 1988 , the price of commodity x was 4.20 and that of y was 6.30 , in which year will commodity x cost 40 paise more than commodity y ?
suppose in β€˜ n ’ years the price of comodity x will be more by 40 paise than that of commodity y . ∴ 420 + 40 n – 630 – 15 n = 40 or , 25 n – 210 = 40 or , 25 n = 250 or , n = 250 ⁄ 25 = 10 years . answer b
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 300", "rs . 200", "rs . 250", "rs . 350" ] }
[ "C" ]
if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 925 will be :
"z share = z , y = 1.2 z x = 1.25 Γ£ β€” 1.2 z , x + y + z = 925 ( 1.25 Γ£ β€” 1.2 + 1.2 + 1 ) z = 925 3.7 z = 925 , z = 250 answer : . c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2984", "2983", "2982", "2981" ] }
[ "A" ]
3034 - ( 1002 / 20.04 ) = ?
option a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 30,000", "rs . 50,000", "rs . 60,000", "rs . 80,000" ] }
[ "A" ]
x and y invested in a business . they earned some profit which they divided in the ratio of 1 : 3 . if x invested rs . 10,000 . the amount invested by y is
"solution suppose y invested rs . y then , 10000 / y = 1 / 3 Γ’ € ΒΉ = Γ’ € ΒΊ y = ( 10000 Γ£ β€” 3 / 1 ) . Γ’ € ΒΉ = Γ’ € ΒΊ y = 30000 . answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 2000", "rs . 10,000", "rs . 18,000", "rs . 20,000" ] }
[ "C" ]
a man took a loan from a bank at the rate of 10 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
"solution principal = rs . ( 100 x 5400 / 10 x 3 ) = rs . 18000 . answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 200", "rs . 250", "rs . 300", "rs . 150" ] }
[ "C" ]
the cost of 3 pens and 5 pencils is rs . 100 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?
"explanation : let the cost of one pen is β€˜ 5 x ’ and pencil is β€˜ x ’ 3 x 5 x + 5 x = rs . 100 15 x + 5 x = rs . 100 x = 100 / 20 = 5 : . cost of 1 pen = 5 x = 5 x 5 = 25 : . cost of 12 pens , i . e . ( one dozen ) = 25 x 12 = rs . 300 answer : option c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "75 m .", "80 m .", "150 m .", "142 m ." ] }
[ "D" ]
a runs twice as fast as b and gives b a start of 71 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 71 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 71 m is 71 / 1 = 71 m so the total time taken by a and b to reach = 2 * 71 = 142 m answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "9 : 5", "2 : 3", "4 : 7", "5 : 6" ] }
[ "A" ]
a dog takes 3 leaps for every 5 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
"explanation : dog : hare = ( 3 * 3 ) leaps of hare : 5 leaps of hare = 9 : 5 . answer : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 1200", "rs . 1500", "rs . 1920", "rs . 2000" ] }
[ "C" ]
a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3200 , a will get :
"explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 128 so , a ’ s amount = 120 Γ— 15 = rs . 1920 . answer : option c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "160", "152", "156", "144" ] }
[ "A" ]
the ratio of ducks and frogs in a pond is 35 : 39 respectively . the average number of ducks and frogs in the pond is 152 . what is the number of frogs in the pond ?
solution : ratio of ducks and frogs in pond , = 35 : 39 . average of ducks and frogs in pond , = 152 . so , total number of ducks and frogs in the pond , = 2 * 152 = 304 . therefore , number of frogs , = ( 304 * 39 ) / 74 = 160 . answer : option a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "22 hours", "21 hours", "24 hours", "23 hours" ] }
[ "C" ]
a cistern is fille in 8 hours and it takes 12 hours when there is a leak in its bottom . if the cistern is full , in what time shall the leak empty it ?
explanation : work done by 1 hour by filling pipe = 1 / 8 work done by 1 hour by the leak and the filling pipe = 1 / 12 work done by 1 hour by the leak = 1 / 8 – 1 / 12 = 1 / 24 hence the leak can empty it in 24 hours . answer : option c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "20", "49", "22", "23" ] }
[ "B" ]
the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 20000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
"sol . let the total number of workers be x . then , 8000 x = ( 20000 Γ— 7 ) + 6000 ( x – 7 ) β€Ή = β€Ί 2000 x = 98000 β€Ή = β€Ί x = 49 . answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2 / 5", "3 / 5", "1 / 6", "1 / 7" ] }
[ "C" ]
what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 6
"explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 6 = . 833 so biggest is 5 / 6 and smallest is 2 / 3 their difference is 5 / 6 - 2 / 3 = 1 / 6 option c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "30 %", "51 %", "90 %", "100 %" ] }
[ "B" ]
in a restaurant , the profit is 130 % 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 . 130 , s . p . = rs . 230 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 230 . profit = rs . ( 230 - 112 ) = rs . 118 . required percentage = ( 118 / 230 * 100 ) % = 51 % appox answer : b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "72.85", "74.31", "72.43", "73.43" ] }
[ "A" ]
a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 36 instead of 66 then find the correct average marks up to two decimal places .
total marks = 35 x 72 = 2520 corrected total marks = 2520 - 36 + 66 = 2550 correct average = 2550 / 35 = 72.85 answer : a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1 : 25', '", "1.225', '", "1 : 52', '", "1 : 522', '" ] }
[ "A" ]
a cube of edge 5 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 * 5 * 5 = 1 / 25 = 1 : 25 . answer a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 15000", "rs . 12000", "rs . 10000", "rs . 20000" ] }
[ "C" ]
the difference b / w the compound interest payble half yearly and the simple interest on a certain sum lent out at 10 % p . a for 1 year is rs 25 . what is the sum ?
in simple words s . i = ptr / 100 = ( p * 1 * 10 ) / 100 p / 10 here amount a = p + s . i = p + p / 10 = 11 p / 10 . . . . now for compound interest when calculated half yearly amount = p [ 1 + r / 200 ] ^ 2 t = p [ 1 + 10 / 200 ] ^ 2 * 1 = 441 p / 400 here its given in the question dat diff btwn simple interest and co...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "450 gms", "100 gms", "300 gms", "240 gms" ] }
[ "D" ]
what is 50 % of 40 % of 1200 grams ?
"50 / 100 Γ— 40 / 100 Γ— 1200 = 240 answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "72 kg", "60 kg", "72 kg", "96 kg" ] }
[ "A" ]
a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1.2 cm when a man gets on it . the mass of man is
"solution volume of water displaced = ( 3 x 2 x 0.012 ) m 3 = 0.072 m 3 . mass of man = volume of water displaced Γ— density of water = ( 0.072 Γ— 1000 ) kg = 72 kg . answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1 1 / 5 min", "4 1 / 5 min", "3 1 / 5 min", "2 1 / 5 min" ] }
[ "A" ]
how many minutes does aditya take to cover a distance of 400 m , if he runs at a speed of 20 km / hr ?
explanation : we know that , time = distance / speedspeed = 20 km / hr = 20 x 5 / 18 m / sec = 509 m / sectime = ( 400 x 9 / 50 ) = 72 sec = 1 1 / 5 min answer : a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs 48000", "rs 47000", "rs 47400", "rs 48400" ] }
[ "D" ]
in business , a and c invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by a and b was 3 : 2 , if rs 157300 was their profit , how much amount did b receive .
"explanation : a : b = 3 : 2 = 6 : 4 = > a : c = 2 : 1 = 6 : 3 = > a : b : c = 6 : 4 : 3 b share = ( 4 / 13 ) * 157300 = 48400 option d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "4 / 13", "1 / 52", "1 / 4", "1 / 5" ] }
[ "A" ]
from a pack of 52 cards , 1 card is drawn at random . find the probability of a face card drawn
"explanation : total number of cases = 52 total face cards = 16 [ favourable cases ] so probability = 16 / 52 = 4 / 13 answer : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "8.5 kmph", "16.0 kmph", "22.5 kmph", "18.6 kmph" ] }
[ "D" ]
john took a bus from home to market , that travels at 50 kmph . while walking back at 5 kmph , halfway through , he suddenly realized he was getting late and he cycled back the remaining distance in 35 kmph . find the average speed .
let the distance be 2 x ( one way ) time taken by bus = 2 x / 50 , by walking = x / 5 , by cycling = x / 35 hours : . average speed = total distance / total time = 5 x / x / 25 + x / 5 + x / 35 = 5 * 60 / 2.4 + 12 + 1.7 = 18.6 answer : d
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "- 3", "- 1", "- 1 / 3", "0" ] }
[ "B" ]
line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 6 ) . what is the slope of line m ?
"ans : b solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 8 ) . midpoint is ( 4 , - 1 ) as we can see that the y axis of intercept point is ( 0 , - 2 ) means line m is parallel to x axis slope m = - 1 ans : b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "51 : 53", "52 : 53", "53 : 54", "54 : 55" ] }
[ "A" ]
the cash difference between the selling prices of an article at a profit of 2 % and 6 % is rs 3 . the ratio of two selling prices is
"explanation : let the cost price of article is rs . x required ratio = ( 102 % of x ) / ( 106 % of x ) = 102 / 106 = 51 / 53 = 51 : 53 . answer : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2 : 3", "5 : 3", "6 : 7", "9 : 16" ] }
[ "B" ]
two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 25 hours respectively . the ratio of their speeds is :
"let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = Γ’ Λ† Ε‘ b : Γ’ Λ† Ε‘ a = Γ’ Λ† Ε‘ 25 : Γ’ Λ† Ε‘ 9 = 5 : 3 . answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "11 : 17", "8 : 27", "5 : 9", "2 : 9" ] }
[ "B" ]
if a : b = 2 : 3 , b : c = 4 : 5 and c : d = 5 : 9 then a : d is equal to :
"solution : a / d = ( a / b ) * ( b * c ) * ( c / d ) = ( 2 / 3 ) * ( 4 / 5 ) * ( 5 / 9 ) = ( 2 * 4 * 5 ) / ( 3 * 5 * 9 ) = 8 / 27 . answer : option b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "0.68", "0.086", "0.86", "0.068" ] }
[ "C" ]
( 0.96 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.96 ) ( power 2 ) + 0.096 + ( 0.1 ) ( power 2 ) is :
"given expression = ( 0.96 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.96 ) ( power 2 ) + ( 0.96 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.96 - 0.1 ) = 0.86 answer is c ."
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1008", "1015", "1022", "1032" ] }
[ "B" ]
the smallest number which when diminished by 7 , is divisible by 12 , 16 , 18 , 21 and 28 is
"solution required numbers = ( l . c . m of 12 , 16,18 , 21,28 ) + 7 β€Ή = β€Ί 1008 + 7 = 1015 . answer b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 9718.27", "rs . 9750", "rs . 10123.20", "rs . 10483.20" ] }
[ "A" ]
what will be the compound interest on a sum of rs . 24,000 after 3 years at the rate of 12 % p . a . ?
"amount = [ 24000 * ( 1 + 12 / 100 ) 3 ] = 24000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 33718.27 c . i . = ( 33718.27 - 24000 ) = rs . 9718.27 answer : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "14 kmph", "12 kmph", "18 kmph", "1 kmph" ] }
[ "C" ]
a man can row 36 kmph in still water . it takes him thrice as long to row up as to row down the river . find the rate of the stream ?
explanation : let man ' s rate upsteam be x kmph then his rate of downstream = 3 x kmph rate still water = 1 / 2 ( 3 x + x ) = 2 x 2 x = 36 x = 18 rate of upstream = 18 rate of downstream = 54 rate of stream 1 / 2 ( 54 - 18 ) = 18 kmph answer : option c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "9", "18", "17", "13" ] }
[ "D" ]
how many multiples of 5 are there between 5 to 75 ?
"explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 . answer : d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "260', '", "262', '", "270', '", "272', '" ] }
[ "C" ]
a swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side . its volume is :
explanation : volume will be length * breadth * height , but in this case two heights are given so we will take average , volume = ( 12 βˆ— 9 βˆ— ( 1 + 4 / 2 ) ) m 312 βˆ— 9 βˆ— 2.5 m 3 = 270 m 3 option c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "10 %", "10.5 %", "11 %", "12.5 %" ] }
[ "A" ]
a trader marked the selling price of an article at 10 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
"sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . ∴ discount % = [ 11 / 110 * 100 ] % = 10 % answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "15 / 16", "1 / 16", "7 / 8", "9 / 8" ] }
[ "A" ]
a and b play a game where each is asked to select a number from 1 to 16 . if the two numbers match , both of them win a prize . find the probability that they will not win a prize in a single trial .
explanation : a and b win a prize , only if both a and b select the number . so , if a chooses a number , b has to select the same number . hence , it is problem on dependent event . let a select a number . , then p ( a ) = 1 / 16 = probability of a . now , b selects the same number after a has already selected that nu...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "800", "900", "1000", "1100" ] }
[ "C" ]
there are 400 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 ) + 400 ( 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 + 400 = 2 / 5 t , or 2 / 5 ( t - m ) = 400 , from here we get that t - m = 1000 , that would be...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "82 %', '", "78 %', '", "80 %', '", "90 %', '" ] }
[ "A" ]
the length and breadth of a square are increased by 40 % and 30 % respectively . the area of the rectangle so formed exceeds the area of the square by ?
since side 1 x side 2 = area therefore , net % change in area = ( x + y + xy / 100 ) % = [ 40 + 30 + ( 40 x 30 ) / 100 ] % or 82 % . therefore , area is increased by 82 % . answer : a
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "15 m', '", "22.5 m', '", "25 m', '", "30 m', '" ] }
[ "C" ]
the length of a rectangualr hll is 5 m more than its breadth . the area of the hall is 750 m . the length of the hall is
solution let the length = xmetres . then length = ( x + 5 ) metres . then , x ( x + 5 ) = 750 = x Β² + 5 x - 750 = 0 ( x + 30 ) ( x - 25 ) = 0 x = 25 . answer c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "350 m", "200 m", "400 m", "700 m" ] }
[ "D" ]
a thief is spotted by a policeman from a distance of 175 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 175 m / 1000 ) x 1 / 2 hr = 7 / 80 hr . in 7 / 80 hrs , the thief covers a distance of 8 x 7 / 80 km = 7 / 10 km = 700 m answer is d .
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "362.33", "399.6", "702.33", "702" ] }
[ "B" ]
. 3 + 33 + 333 + 33.3 = ?
". 3 33 333 33.3 - - - - - - - - - - 399.6 - - - - - - - - - - answer is b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "10", "100", "1000", "10000" ] }
[ "C" ]
( 1000 ) 7 Γ· ( 10 ) 18 = ?
"explanation : = ( 103 ) 7 / ( 10 ) 18 = ( 10 ) 21 / ( 10 ) 18 = 10 ( 3 ) = 1000 option c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "25.6 %", "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 . 462 ?
"cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 462 , discount = 621 - 462 = 159 discount % = 159 / 621 * 100 = 25.6 % answer : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "2736900", "2738800", "2658560", "2716740" ] }
[ "B" ]
8796 x 223 + 8796 x 77 = ?
"= 8796 x ( 223 + 77 ) ( by distributive law ) = 8796 x 300 = 2638800 answer is b"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "5600", "600", "6400", "7200" ] }
[ "C" ]
how many bricks each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall 8 m x 6 m x 22.5 m
"explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 25 x 11.25 x 6 ) = 6400 answer : c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "5655", "1366", "6444", "7266" ] }
[ "B" ]
how many bricks each measuring 30 cm x 12 cm x 10 cm , will be needed to build a wall 6 m x 4 m x 20.5 m
explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 600 x 400 x 20.5 ) / ( 30 x 12 x 10 ) = 1366 answer : b
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "40", "54", "50", "39" ] }
[ "C" ]
a worker makes a toy in every 2 h . if he works for 100 h , then how many toys will he make ?
"no . of toys = 100 / 2 = 50 answer : c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "115 min", "215 min", "315 min", "415 min" ] }
[ "A" ]
how many minutes does aditya take to cover a distance of 400 m , if he runs at a speed of 20 km / hr
"explana Ι΅ on : we know that , time = distancespeedspeed = 20 km / hr = 20 βˆ— 518 m / sec = 509 m / sec time = ( 400 βˆ— 950 ) = 72 sec = 115 min answer : op Ι΅ on a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "9", "15", "36", "45" ] }
[ "C" ]
two numbers are in ratio 4 : 5 and their lcm is 180 . the smaller number is
solution : let two numbers be 4 x and 5 x ; their lcm = 180 and hcf = x ; now , 1 st number * 2 nd number = lcm * hcf or , 4 x * 5 x = 180 * x ; or , 20 x = 180 ; or , x = 9 ; then , the smaller number = 4 * 9 = 36 . answer : option c
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "16 : 5", "14 : 5", "16 : 7", "19 : 5" ] }
[ "D" ]
two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 2 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
"quantity of alcohol in vessel p = 62.5 / 100 * 2 = 5 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 / 4 + 7 / 2 = 19 / 4 = 4.75 litres as 6 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5 . a...
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "225.623", "224.777", "233.523", "414.637" ] }
[ "A" ]
893.7 – 573.07 – 95.007 = ?
"solution given expression = 893.7 - ( 573.07 + 95.007 ) = 893.7 - 668.077 = 225.623 . answer a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "3 : 4", "3 : 5", "11 : 8", "16 : 15" ] }
[ "C" ]
a man invests some money partly in 12 % stock at 132 and partly in 10 % stock at 80 . to obtain equal dividends from both , he must invest the money in the ratio :
"solution for an income of rs . 1 in 12 % stock at 132 , investment = rs . ( 132 / 12 ) = rs . 11 . for an income of rs . 1 in 10 % stock at 80 , investment = rs . ( 80 / 10 ) = rs . 8 . ∴ ratio of investments = 11 : 8 = 11 : 8 answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1 : 4', '", "1 : 16', '", "4 : 1', '", "16 : 1', '" ] }
[ "D" ]
spheres a and b have their radil 40 cm and 10 cm respectively . the ratio of the surface area of a to the surface area of b is
solution let the radil of a and b be r and r respectively . required ratio = 4 Ο€ r 2 / 4 Ο€ r 2 β€Ή = β€Ί r 2 / r 2 β€Ή = β€Ί ( r / r ) 2 β€Ή = β€Ί ( 40 / 10 ) 2 β€Ή = β€Ί 16 : 1 . answer d
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "1 / 2", "1 / 4", "3 / 4", "2 / 3" ] }
[ "A" ]
if a * b * c = 130 , b * c * d = 65 , c * d * e = 1000 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?
"explanation : a βˆ— b βˆ— c / b βˆ— c βˆ— d = 130 / 65 = > a / d = 2 d βˆ— e βˆ— f / c βˆ— d βˆ— e = 250 / 1000 = > f / c = 14 a / d * f / c = 2 * 1 / 4 = 1 / 2 answer : a"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "960", "1005", "1,200", "920" ] }
[ "B" ]
the profit earned by selling an article for 892 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 892 – x = 448 + x or , x = 444 ⁄ 2 = 222 \ cost price of the article = 892 – x = 448 + x = 670 \ sp of the article = 670 Γ— 150 ⁄ 100 = 1005 answer b
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "720", "900", "1200", "1800" ] }
[ "C" ]
a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is
"solution 2 ( 15 + 12 ) Γ— h = 2 ( 15 x 12 ) β€Ή = β€Ί h = 180 / 27 m = 20 / 3 m volume = ( 15 Γ— 12 Γ— 20 / 3 ) m 3 β€Ή = β€Ί 1200 m 3 . answer c"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 120", "rs . 160", "rs . 240", "rs . 300" ] }
[ "D" ]
a sum of rs . 1700 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
"explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 1700 = > 17 x / 12 = 1700 = > 1700 x 12 / 17 = rs . 1200 hence , b ’ s share = rs . ( 1200 / 4 ) = rs . 300 . answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "10200", "10000", "9500", "9000" ] }
[ "B" ]
on a certain island , 5 % of the 10000 inhabitants are one - legged and half of the others go barefooted . what is the least number of shoes needed in the island ?
explanation : = > one - legged = 5 % of 10000 = 500 = > remaining = 10000 - 500 = 9500 = > barefooted = 9500 / 2 = 4750 = > remaining people = 9500 - 4750 = 4750 = > hence required number of shoes = 4750 * 2 + 500 * 1 = 10000 hence ( b ) is the correct answer . answer : b
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 500", "rs . 600", "rs . 650", "rs . 720" ] }
[ "D" ]
a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if the company declares 6 % 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 . ( 6 / 100 x 12000 ) = rs . 720 . answer d"
MathQA
{ "label": [ "A", "B", "C", "D" ], "text": [ "rs . 1386", "rs . 1764", "rs . 1650", "rs . 2268" ] }
[ "C" ]
the true discount on a bill due 9 months hence at 16 % per annum is rs . 198 . the amount of the bill is
"solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 198 . ∴ x 16 x 9 / 12 x 1 / 100 } = 198 or x = 1650 . ∴ p . w . = rs . 1650 . answer c"
MathQA