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Aptitude Question Of the day

August 21 2017
Question With a uniform speed a car covers a distance in 8 hours. If the speed is increased by 4 km/hr the same distance could be covered in 15/2 hours. What is the distance covered?
Answer

Here, (D/7.5) – (D/8) = 4 (where D is the distance in km)

Thus 0.5 D = 4 x 8 x 7.5

So, D = 2 x 4 x 8 x 7.5 = 480 km

Previous Question
  • August 20 2017
    QuestionN number of persons decides to raise Rs. 3 lakhs by equal contributions from each. If they contributed Rs. 50 each extra, the contribution would be Rs. 3.25 lakhs. How many persons are there?
    Answer

    Required person = (325000 – 300000)/50 = 500

  • August 19 2017
    QuestionA grosser purchase 80kg of rice at 13.50 per kg and mixed it with 120 kg rice at Rs. 16 per kg. at what rate per kg should he sell the mixture to gain 16%?
    Answer

    C.P. of 200 kg of mix = Rs. (80*13.50 + 120*16) = Rs. 3000.

    S.P. = 116% of Rs 3000 = Rs. (116*3000/100) = Rs. 3480.

    Rate of S.P. of the mixture = Rs. 3480/200 per kg. = Rs. 17.40 per kg

  • August 18 2017
    QuestionMilk contains 5% water. What quality of pure milk should be added 10 litres of milk to reduce this 2%?
    Answer

    Here the required quantity of pure milk

    = [10*(5 – 2)]/2

    = (10*3)/2 = 15 litres

  • August 17 2017
    QuestionIn a two digit number the digit in the unit’s place is twice the digits in the ten’s place and the number obtained by interchanging the digits is more than the original number by 27. What is the 50% of original number?
    Answer

    let the ten’s digit be x

    Therefore Unit’s Digit = 2x

    So the original number =10x + 2x =12x

    On interchanging the digits, the new number = 10*2x + x = 21x

    According to the question

    21x – 12x = 27

    Thus x= 3

    Therefore original number = 12*3 = 36

  • August 16 2017
    QuestionTwo persons A and B working together can dig a trench in 8 hours, while A alone can dig it in 12 hours. In how many hours B alone can dig such a trench?
    Answer

    (A + B)s one hour work = 1/8

    Work done by A in one hour = 1/12

    Therefore, work done by B in one hour = (1/8) - (1/12) = 1/24.

    Hence, B alone can dig the trench in 24 hours

  • August 15 2017
    QuestionStarting with a initial speed of 30 km/hr, the speed is increased by 4 km/hr every 2 hours. How many hours it will take to cover a distance of 288 km?
    Answer

                    Hour                      Speed (Km/hr)                  Distance travelled (In Km)

                      2                              30                                           60

                      2                              34                                           68

                      2                              38                                           76

                      2                              42                                           84
    _______________________________________________________________________________

                      8                                                                            288
    ________________________________________________________________________________

     

    Hence, the required time = 8 hours

  • August 14 2017
    QuestionA and B can do a piece of work in 12 days; B and C can do it in 15 days and A and C in 20 days. In how many days will A, B and C finishes it working all together?
    Answer

    work done by (A + B) in one day = 1/12

    similarly work done by (B + C) in one day = 1/15 and by (A + C) = 1/20

    Adding,  we get: 2(A + B + C) = (1/12 + 1/15 + 1/20) = 1/5 => (A + B + C) = 1/10

    Thus, A, B and C together can finish work in 10 days.

  • August 13 2017
    QuestionA zookeeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of animals he found it to be 260. If the zoo had only parrot and zebra, how many zebra were in the zoo?
    Answer

    Let the number of Zebras = x

    Then the number of Parrots = 80 - x

    Each Parrot has 2 legs and each zebra has 4 legs.

    therefore, total number of legs = 4x + 2(80 - x) = 260

    so, 4x + 160 - 2x = 260

    => 2x = 100

    so x = 50

    Thus the number of Zebras in the zoo = 50

     

  • August 12 2017
    QuestionA shopkeeper offered a discount of 15% on the labelled price. By selling an article for Rs. 340 after giving discount he earned a profit of 40/3%. What would have been the percent profile earned if no discount was offered.
    Answer

    Let the marked price be Rs. x

    Then, 85% of x =340

    Thus, 85x/100 = 340 so x = Rs. 400

    Therefore C.P. = [100/(100 + gain%)]*S.P.

    = [100/(100 + 40/3)]*340

    = Rs. 300

    Therefore required gain percentage = [(400 – 300)/300]*100 =100/3 =33 (1/3)

  • August 11 2017
    Question2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?
    Answer

    Let 1 man do work in one day = x

    and 1 boy do work in one day = y

    Then, 2x + 3y = 1/10 and 3x + 2y = 1/8.

    solving, we get: x = 7/200 and y = 1/100.

    Therefore (2 men + 1 boy) one day work = (2* 7/200) + (1* 1/100) = 16/200 = 2/25.

    So. 2 men and a boy together can finish the work in 25/2 days

  • August 10 2017
    QuestionFree notebooks were distributed equally among the children of a class. The number of notebooks each children was one eighth of the number of the children when the number of children been half, each would have got 16 notebooks. How many notebooks was distributed in all?
    Answer

    let the number of children = x

    Hence total number of books distributed = (1/8)*x*x = x2/8 …. (i)

    In case II: No. of children =x/2

    Now the total number of notebooks =16 * (x/2) = 8x…. (ii)

    Comparing (i) and (ii), we get

    x2/8 = 8x or x = 64

    Hence total no. of notebooks

    = (64 * 64)/8 =512

  • August 09 2017
    QuestionOn sports day, if 30 children were made to stand in a column, 16 columns could be formed. If 24 children were made to stand in a column, how many columns could be formed?
    Answer

    Total number of children = 30*16 = 480

    number of columns of 24 children each = 480/24 =20

  • August 08 2017
    QuestionA train of length 150 m takes 10 sec to cross another train 100 m long coming from the opposite direction. If the speed of first train is 30 km/hr. what is the speed of second train?
    Answer

    Time taken to cross the trains = (150 + 100)/[(25/3) + x], where x is the speed of train.

    Therefore, 10 = (250 * 3)/(25 + 3x)

    250 + 30x = 750

    30x = 500

    x = 50/3 m/s

    therefore, x = (50/3) * (18/5) = 60 km/hr

  • August 07 2017
    QuestionSanjeev started a business by investing Rs. 36000. After 3 months Rajiv joined him by investing Rs. 36000. Out of annual profit of Rs. 37100, find the share of each?
    Answer

    Ratio of their capitals = 36000*12 : 36000*9 = 4 : 3

    Share of Sanjiv = Rs. (37100* 4/7) = Rs. 21200

    Share of Rajiv = Rs. (37100* 3/7) = Rs.  15900

  • August 06 2017
    QuestionThe difference between a two-digit number and the number obtained by interchanging the digits is 9. What is the difference between the two digits of the number?
    Answer

    Suppose the two-digit number be 10x + y.

    Then we have been given

    10x + y – (10y + x) = 9

    Thus, 9x – 9y = 9

    x – y = 1

    Hence, the required difference = 1

    Note: If the difference between a two-digit number and the number obtained by interchanging the digits is D, then the difference between the two digits of the number = D/9

  • August 05 2017
    QuestionA bag contains Rs. 114 in the form of 1 rupee, 50 paisa and 10 paisa coins in the ratio 3 : 4 : 10. What is the number of 50 paisa coins?
    Answer

    Ratio of values of the coins = 3/1 : 4/2 : 10/10

    = 30 : 20 : 10

    Values of 50 paise coin = 114 * (20/60) = Rs. 38

    Number of 50 paise coin = 38 * 2 = 76

  • August 04 2017
    QuestionThe difference between a number and its three-fifths is 50. What is the number?
    Answer

    Suppose the number is N

    Then N – (3/5)N = 50

    Thus, 2N/5 = 50

    Therefore N = (50*5)/2 = 125

  • August 03 2017
    QuestionA boat running downstream covers a distance of 16kms in 2 hours, while for covering the same distance upstream it takes 4 hours. What is the speed of the boat in the still water?
    Answer

    Time = distance/speed

    Let speeds of boat and river be x and y respectively

    Therefore 2 = 16/(x + y) and 4 = 16/(x – y)

    i.e. (x + y)/(x – y) = 2, i.e. x =3y

    Put x =3y we got

    2 = 16/(3y + y)

    y = 2 and x = 6

    thus the speed of boat in still water is 6 km/hr

  • August 02 2017
    Question12 men can complete a work in 36 days, 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only women to complete the remaining piece of work in 4 days, how many women would be required?
    Answer

    12 x 36 men can do the work in one day

    = 18 x 60 women can do the same in one day

    Or 12 x 36 Men = 18 x 60 women

    Or 2 men = 5 women

    Therefore 8 men = 20 women

    8 men + 20 women = 20 + 20 = 40 women

    18 women can do a work in 60 days

    So 40 women can do the work in (60 x 18)/40 = 27 days

    Work done by 40 women in 1 day = 1/27

    Work done by 40 women in 20 days = 20/27

    Remaining work = 1 – 20/27 = 7/27

    Work                     Days                      Women

    1                              60                           18

    7/27                         4                              n

    Thus less work less women
    1 : 7/27 :: 18 : n

    And less days more women

    4 : 60 :: 18 : n

    1 x 4 x n = 18 x 7/27 x 60

    Therefore n = 70

  • August 01 2017
    Question5/9 part of the population in a village are males. If 30% of the males are married, the percentage of unmarried females in the total population is:
    Answer

    Let the population = x => Males = (5/9)x

    Married Males = 30% of (5/9)x = x/6

    Married females = x/6

    Total females = {x - (5/9)x} = 4x/9

    Unmarried females = (4x/9) - (x/6) = 5x/18

    Required percentage = (5x/18)* 1/x * 100 = (259/9) %

  • July 31 2017
    QuestionP can give Q a start of 20 seconds in a kilometre race. P can give R a start of 200 meters in the same race. And Q can give R a start of 20 seconds in that same race. How long does P take to run the kilometre?
    Answer

    P can give Q a start of 20 sec in a kilometer race. So, if Q takes 'x' seconds to run a kilometer, then P will take x - 20 seconds to runthe kilometer.

    Q can give R a start of 20 seconds in a kilometer race. So, if R takes 'y' seconds to run in a kilometer, then Q takes y - 20 seconds to run the kilometer.

    we know Q takes x seconds to run a kilometer,

    therefore, x = y - 20

    therefore, P will take x - 20 = y - 20 - 20 = y - 40 seconds to run a kilometer.

    i.e. P can give R a start of 40 seconds to run a kilometer race, as R takes y seconds to run a kilometer and P takes only y - 40 seconds to run the kilometer.

    We also know thet P can give R a start 200 meters in a km race. This is essentially means that R runs 200 meters in 40 seconds.

    Therefore, R will take 200 seconds to run a km.

    if R takes 200 seconds to run a km, then P will take 200 - 40 = 160 seconds to run a km.

     

     

  • July 30 2017
    QuestionA man is standing on a railway bridge which is 180 m long. He finds that a train crossed the bridge in 20 sec but himself in 8 seconds. Find the length of the train and its speed?
    Answer

    Let the length of the train be x meters

    Then, the train covers x meter in 8 seconds and (x + 180) meters in 20 seconds.

    Therefore x/8 = (x + 180)/20 => 20x = 8(x + 180) => x = 120.

    Therefore the speed of train = 120m

    Speed of train = 120/8 m/sec = 15 m/sec = 15 * (18/5) kmph = 54 kmph

     

     

  • July 29 2017
    QuestionIf [1/(x + 1)] + [2/(y + 2)] + [1009/(z + 1009)] = 1, then the value of [x/(x + 1)] + [y/(y + 2)] + [z/(z + 1009)]?
    Answer

    [1/(x + 1)] + [2/(y + 2)] + [1009/(z + 1009)] = 1

    Therefore [1/(x + 1)] – 1 + [2/(y + 2)] – 1 + [1009/(z + 1009)] – 1 = 1 – 3

    -[x/(x + 1)] - [y/(y + 2)] - [z/(z + 1009)] = -2

    Therefore, [x/(x + 1)] + [y/(y + 2)] + [z/(z + 1009)] = 2

  • July 28 2017
    QuestionPawan travelled 1200km by air which formed 2/5 of his trip. One third of the whole trip, he travelled by car ant the rest by train. The distance travelled by train was?
    Answer

    Let the total trip be x km.

    then, 2x/5 = 1200

    x = 1200*5/2 = 3000km

    Distance travelled by car = (1/3)*3000 = 1000 km

    Journey by train = [3000-(1200+1000)] = 800km

     

  • July 27 2017
    QuestionA candidate who gets 20% marks fails by 10 marks but another candidate who gets 42% marks gets 12% more than the passing marks. Find the maximum marks?
    Answer

    Let the maximum marks be x.

    From the given statement pass percentage is 42% -12% = 30%

    By hypothesis, 30% of x - 20% of x =10(marks)

    i.e., 10% of x = 10

    Therefore, x = 100 marks

  • July 26 2017
    QuestionA train running at 54kmph takes 20 seconds to pass a platform. Next it takes 12 second to pass a man walking at 6kmph in the same direction in which the train is going. Find the length of the train and the length of the platform.
    Answer

    Let the length of the train be x meters and the lengthn of the platform be y meters.

    Speed of the train relative to man = (54 - 6) kmph = 48 kmph = 48 * (5/18) m/sec = 40/3 m/sec

    In passing a man, the train covers its own length with relative speed.

    Therefore, length of the train = (Relative speed * time) = (40/3)*12 m = 160m

    also, speed of the train = (54 * 5/18) m/sec = 15 m/sec

    Therefore, (x + y)/15 = 20 or x + y = 300

    or y = (300 - 160) = 140 meter.

    Therefore Length of train = 160 m

    and Length of platform = 140 m

  • July 25 2017
    QuestionA group of workers can do a task in 24 days. However as 7 of them were absent it taken 30 days to complete the work. How many people actually worked on the job to complete it?
    Answer

    Let the originalnumber of workers in the group be 'x'

    Therefore, actual number of workers = x - 7

    We know that the number of manhours required to do the job is the same in both cases.

    Therefore, x(24) = (x - 7)*30

    24x = 30x - 210

    6x = 210

    x = 35

    therefore, the actual number of workers who worked to complete the job = x - 7 = 35 - 7 = 28

  • July 24 2017
    QuestionWhat is the sum of positive integers less than 100 which leave a reminder 1 when divided by 3 and leave a remainder 2 when divided by 4?
    Answer

    required numbers are

    10, 22, 34, 46, 58, 70, 82, 94

    Therefore, total sum is 416

  • July 23 2017
    Question1. A three digit number consists of 9, 5 and one more number. When these digits are reversed and then subtracted from the original number the answer yielded will be consisting of same digits arranged yet in different order. What is the other digit?
    Answer

    Let the digit unknown be n.

    The given number is then, 900+50+n = 950+n

    When reserved, the new number is 100n+50+9 = 59+100n.

    subtracting these two numbers we get 891 - 99n

    the digit can be arranged in 3 ways or 6 ways.

    we already investigated 2 of these ways.

    we can now try one of the remaining 4 ways. one of these is n95

    100n+90+5 = 891 - 99n

    or 199n = 796

    so n =4

    thus the unknown digit is 4

  • July 22 2017
    QuestionWhat is the total number of three digit numbers with unit digit 7 and divisible by 11?
    Answer

    The total numbers of three digit numbers with unit digit 7 and divisible by 11 are

    187, 297, 407, 517, 627, 737, 847, 957

    i.e. total 8 numbers.

  • July 21 2017
    QuestionThe ratio of marks obtained by Ajay and Vijay is 6:5. If the combined average of their percentage is 68.75 and their sum of the marks is 275, find the total marks for which exam was conducted?
    Answer

    Let Ajay's marks be 6x and Vijay's marks is 5x. Therefore, the sum of the marks  = 6x + 5x = 11x.

    But the sum of the marks is given as 275 = 11x. we get x = 25

    Therefore Ajay marks is 6x = 150

    and Vijay marks = 5x = 125.

    Therefore, the combined average of their marks  = (150 + 125)/2 = 137.5

    If the total marks of the exam is 100 then their combined average of percentage is 68.75.

    Therefore, if their combined average of their percentage is 137.5 then the total marks would be

    (137.5/68.75)*100 = 200

  • July 19 2017
    QuestionIf (x/y) = (z/w), Then what is (xy + zw)^2 equal to?
    Answer

    Given, x/y = z/w => xw = yz

    Now, (xy + zw)2 = x2y2 + z2w2 + 2(xy * zw)

    = x2y2 + z2w2 + 2(yz * yz)

    = x2y2 + y2z2 + z2w2 + y2z2

    = y2(x2 + z2) + z2w2 + x2w2

    = y2(x2 + z2) + w2(x2 + z2)

    = (x2 + z2)(y2 + w2)

  • July 16 2017
    QuestionA man bought a horse and a cart. If he sold the horse at 10% loss and the cart at 20% gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him for horse and cart is?
    Answer

    Let x be the cost price of the horse and y be the cost price of the cart. In the first sale there is no losss or profit (i.e.) The loss obtained is equal to the gain.

    Therefore (10/100)*x = (20/100)*y

    => x = 2y         ------------(i)

    In the second sale, he lost Rs. 10. (i.e.) The loss is greater Than the profit by Rs. 10.

    Therefore (5/100)*x = (5/100)*y + 10 -----------------(ii)

    Substituting (i) in (ii), we get

    (10/100)*y = (5/100)*y + 10

    (5/100)*y = 10

    y = 200

    from (i), 2 * 200 = x = 400.

    thus the cost price of Horse = Rs. 400

    And Cost Price of cart = Rs. 200

  • July 12 2017
    QuestionA man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs. 10.50 less, he would have gained 30%. Find the cost price of the article?
    Answer

    Let the C.P. be Rs. x

    1st S.P. = 125% of Rs. x = 125 * (x/100) = 5x/4

    2nd C.P. = 80% of Rs. x = 80 * (x/100) = 4x/5

    2nd S.P. = 130% of 4x/5 = (130/100) * (4x/5) = 26x/25

    Therefore, (5x/4) - (26x/25) = 10.50 or x = 10.50 * (100/21) = 50

    Hence C.P. = Rs. 50

  • July 07 2017
    QuestionA tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. how much time will pipe A alone take to fill the tank?
    Answer

    Here ratio of efficiencies of pipes A, B and C are as follows:

                    C             B             A

                    2              1

                                    2              1
               __________________________

                     4 :           2 :            1

    Suppose the efficiencies of pipes C, B and A are 4K, 2K and K

    Since, the tank is filled in 5 hours by the three pipes having combined efficiency equal to 7K, the time required to fill the tank by A alone = (7K * 5)/K = 35 hours

  • July 06 2017
    QuestionThere are some coins and rings of either gold or silver in a box. 60% of the objects are coins, 40% of the rings are of gold and 30% of the coins are of silver. What is the percentage of gold articles?
    Answer

    If 60% of the objects are coins, then 40% of the objects are rings.

    If 30% of the coins are silver, assume the other 70% are gold.

    70% of the 60% coins = 42% of the total is gold from the coins 40% of the 40% rings = 16% of the total is gold from the rings

    42% + 16% = 58% of the total is gold.

  • July 05 2017
    QuestionFrom height of 8 mts a ball is fell down and each time it bounces half the distance back. What will be the distance travelled by ball.
    Answer

    The total distance travelled by ball = 8+4+4+2+2+1+1+0.5+0.5+...etc = 24

     

  • July 04 2017
    QuestionTwo trains 200mtr and 150mtr are running on the parallel rails at the rate of 40kmph and 45kmph respectively. In how much time will they cross each other if they are running in the same direction.
    Answer

    Relative speed of the train = 45 - 40 = 5 km/hr = 25/18 m/sec

    and the total distance covered = sum of lengths of trains  = 350 m

    So, tome taken = 350 * (18/25) = 252 sec

  • July 02 2017
    QuestionThe average of five consecutive odd numbers is 61. What is the difference between the highest and the lowest number?
    Answer

    suppose the consecutive odd numbers are:

    x, x + 2, x + 4, x + 6, x + 8

    Thus the difference between the highest and the lowest number = x + 8 – x = 8

    Note: While answering the above question does not require the average of the five consecutive odd numbers.

  • July 01 2017
    QuestionThe wheat sold by grocer contained 10% low quality wheat. What quantity of good quality wheat should be added to 150 kgs of wheat so that the percentage of low quality wheat becomes 5%?
    Answer

    From the given conditions,

    10 = (15/150)*100

    And 5 = (15/x)*100
    x = 300

    Therefore addition = 300 – 150 = 150 kg

  • June 26 2017
    QuestionTen years ago, chandravati’s mother was four times older then her daughter. After 10 years, the mother will be twice older than daughter. The present age of Chandravati is?
    Answer

    Let Chandrawathi's age 10 years ago be x years.

    Her mother's age 10 years ago = 4x

    so, according to question,

    (4x+10)+10 = 2(x+10+10)

    thus x = 10

    thus Chandrawati's present age = (x+10) =20 years

  • June 25 2017
    QuestionA fast typist can type some matter in 2 hours and a slow typist can type the same in 3 hours. If both type combinely, in how much time will they finish?
    Answer

    The fast typist do work in one hour = 1/2

    The slower typist do work in one hour  = 1/3

    If they work together, work done in one hour = 1/2 + 1/3 = 5/6

    So, The work will be completed in 6/5 hours i.e. 1 + 1/5 hours = 1 hour 12 mins.

  • June 24 2017
    QuestionA train is running at a speed of 20 meter/sec crosses a pole in 24 sec less that it requires to cross a platform thrice its length at the same speed. What is the length of the train?
    Answer

    Let the length of train = x

    Thus the length of the platform = 3x

    Thus according to the problem

    x/20 = [(x + 3x)/20] – 24

    Therefore x = 160 m

  • June 23 2017
    Question405 sweets were distributed equally among the children in such a way that the number of sweets received by the child is 20% of the total number of children. How many sweets did each child received?
    Answer

    Let, number of children = x

    Then, x * 20% of x = 405

    i.e. x * (x/5) = 405

    or x = 45

  • June 22 2017
    QuestionA 20 litre mixture of milk and water contains milk and water in the ratio 3:2. 10 litre of mixture is removed and replaced with pure milk the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?
    Answer

    The 20 litre mixture contains milk and water in ratio of 3:2.

    therefore, there will be 12 litres of milk in the mixture and 8 liters of water in the mixture.

    STEP 1: When 10 litres of the mixture is removed, 6 liters of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replace with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.

    STEP 2: When 10 litres of the new mixture is removed, 8 liters of milk and 2 litres of water is removed. the container will have 8 litres of milk and 2 liters of water in it. Now 10 litres of pure milk is added.

    therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step.

    Therefore, the ratio of milk and water is 18:9 or 9:1

  • June 21 2017
    QuestionPresent age of Seema and Naresh are in the respective ratio of 5:7. Five years hence the ratio of their ages becomes 3:4 respectively. What is Naresh‘s present age in years?
    Answer

    Let the present age of Seema and Naresh be 5x and 7x years respectively.

    Now according to the question

    (5x + 5)/(7x + 5) = 3/4

    Thus, 21x + 15 = 20x + 20

    So x = 5

    Therefore Naresh’s present age = 7*5 = 35 years

  • June 20 2017
    Question2. Varun’s chain of used furniture dealership sold 570 chairs in 2010. If the chain sold 450 chairs in 2011, by what percent did the number of chairs sold decrease?
    Answer

    Let percentage of decrease is x, then

    570(100 – x)/100 = 450

    so, 57000 - 45000 = 570x

    12000 = 570x 

    so, x = 12000/570 = 21%

  • June 18 2017
    QuestionA man can row 50 km upstream and 72 km downstream in 9 hours. He can also row 70 km upstream and 90 km downstream in 12 hours. Find the rate of current?
    Answer

    Let x and y be the upstream and downstream speed respectively.

    Hence 50/x + 72/y = 9 and 70/x + 90/y = 12

    Solving for x and y we get x = 10 km/hr and  y = 18 km/hr

    We know that Speed of the stream = 1/2 * (Downstream speed - Upstream speed) = 1/2 (18 - 10) = 8/2 = 4 km/hr

  • June 17 2017
    QuestionTwo taps can fill a tub in 5 min and 7 min respectively. A pipe can empty it in 3 min. if all the three are kept open simultaneously, when will the tub be full?
    Answer

    net filling in 1 min = 1/5 + 1/7 – 1/3

    = (21 + 15 – 35)/105

    = 1/105

    Hence, the tub will be full in 105 min.

  • June 12 2017
    QuestionAverage weight of three boys P, T and R is 54 (1/3) while the average weight of three boys T, F and G is 53 Kgs. What is the average weight of P, T, R, F and G?
    Answer

    Total weight of D, T, R = (163/3)*3 = 163

    And total weight of T, F, G = 53 x 3 = 159

    Thus total weight of 6 persons = 163 + 159 = 322kg

    Average weight = 322/6 = 53.66 kg

  • June 10 2017
    QuestionIf a man walks at the rate of 5kmph, he misses a train by only 7 min. however if he walks at rate of 6kmph he reaches the station 5 minutes before the arrival of the train. Find the distance travelled by him to reach the station.
    Answer

    Let the required distance be x km.

    difference in the time taken at two speeds = 12 mins =1/5 hours

    therefore x/5 - x/6 = 1/5

    or 6x - 5x = 6

    or x = 6km

    Hence, the required distance is 6km

  • June 08 2017
    QuestionMr. ‘X’ invested certain amounts in two different schemes ‘A’ and ‘B’. Scheme ‘A’ offers simple interest at 12% pa. And scheme ‘B’ offers compound interest at 10% pa. Interest accrued on the amount invested in scheme ‘A’ in two year was Rs. 3,600 and the total amount invested was Rs. 35,000. What was the interest accrued on the amount invested in scheme ‘B’?
    Answer

    let the amount invested in the scheme A be Rs. x

    Therefore (x*12*2)/100 = 3600

    So, x = Ra. 15000

    Total investment =Rs. 35000

    Therefore amount invested in scheme B = Rs. (35000 - 15000)

    = Rs. 20000

      Therefore C.I. = P[(1 + R/100)T – 1]

    = 20000[(1 + 10/100)2 – 1]

    = 20000[1.21 – 1]

    = Rs. 4200

  • June 07 2017
    QuestionSatish invest Rs. 35,500 in a scheme which earns him simple interest at 15% p.a. for two years. At the end of 2 years he reinvested the principle amount plus interest earned in another scheme which earned him compound interest at 20% p.a. What will be the total interest earned by Satish over the principal amount at the end of 5 years?
    Answer

    S.I. = 35500 x (15/100) x 2 = Rs. 10650

    Now A = 35500 + 10650 = Rs. 46150

    C.I. for 3 years = 46150 [(1 + 20/100)3 – 1] = Rs. 33597.20

    Total Interest = 10650 + 33597.20 = Rs. 44247.20

  • June 06 2017
    QuestionIf 2x + 3y + z = 55, x + z – y = 4 and y – x + z = 12, then what is the value of y?
    Answer

    Given 2x + 3y + z = 55 ….(i)

    x + z – y = 4 …. (ii)

    y – x + z = 12 …. (iii)

    Adding equation (ii) and (iii)

    we get, 2z = 16 so z = 8

    now putting it in equation (i) and (ii), we get

    2x + 3y = 47 … (iv)

    x – y = -4 … (v)

    Multiplying equation (v) by 2 and subtracting it with equation (iv) we get

    y = 11

  • June 04 2017
    QuestionIf s(a) denotes square root of a, find the value of s(12 + s(12 + s(12 + ……… up to infinity.
    Answer

    Let x = s(12 + s(12 + s(12+ ....

    we can write x = s(12 +x)

    i.e. x2 = 12 + x => x2 - x - 12 = 0

    solving the quadratic equation, we get x = -3 or x = 4.

    As sum Cannot be negative so we discard -3 and hence sum = 4

  • June 03 2017
    QuestionA and B enter in to a partnership and A invested Rs. 10,000 in the partnership. At the end of 4 months he withdraws Rs. 2000. At the end of another 5 months, he withdraws another Rs. 3000. If B receives Rs. 9600 as his share of the total profit of Rs. 19,100 for the year, how much did B invested in the company?
    Answer

    The total profit for the year is 19100. Of this B gets Rs. 9600.

    Therefore, A would get (19100 - 9600) = Rs. 9500

    The partners split their profits in the ratio of their investments.

    Therefore, the ratio of the investments of A : B = 9500 : 9600 = 95 : 96

    A invested Rs. 10000 initially for a period of 4 months. Then, he withdrew Rs. 2000

    Hence, his investment decreases to Rs. 8000(for next 5 months).

    Then he withdraws another Rs. 3000. Hence, his investment will stand reduced to Rs. 5000 during the last three months.

    So, the amount of money that he had invested in the company on a money-month basis will be 

    = (4*10000) + (5*8000) + (3*5000) = 40000 + 40000 + 15000 = 95000

    If A had Rs. 95000 money months invested in the company, B would Have had Rs. 96000 money months invested in the company(as the ratio of their investments is 95 : 96).

    If B had Rs. 96000 mioney months invested in the company, he has essentially invested 96000/12 = Rs. 8000

  • May 31 2017
    QuestionThe salary of an employee increases consistently by 50% every year. If his salary today is Rs. 10,000, what will be the salary after another 4 years?
    Answer

    His salary after 4 years

    = 10000(1 + 50/100)4

    = 10000 x (1.5)4

    = Rs. 50625

  • May 30 2017
    QuestionIf 20 men can build a wall 56m long in 6 days, what length of a similar wall can be build by 35 men in 3 days?
    Answer

    Since the length is to be found out, we compare each item with the length as shown below:

    More men, More length Built (Direct)

    Less Days, Less length built (Direct).

    Men 20 :35 :: 56 : x

    Similarly, Days 6 : 3 :: 56 :x

    therefore, 20*6*x = 35*3*56 or x = 49

    Hence, the required length = 49m

  • May 26 2017
    QuestionWhat is the greatest number which divides 392, 486 and 627 so as to leave the same reminder in each case?
    Answer

    when we divide the given numbers by 47 it will give the reminder 16 in each case

  • May 25 2017
    QuestionThe boys and girls in a college are in the ratio of 3:2. If 20% of boys and 25% of girls are adults, the percentage of students who are not adults is?
    Answer

    Suppose boys = 3x and Girls = 2x

    not adults = (80*3x/100) + (75*2x/100) = 39x/10

    thus required percentage = (39x/10)*(1/5x)*100 = 78%

  • May 24 2017
    QuestionSuppose y is equal to the sum of two quantities of which one varies directly as x and the other inversely as x. if y = 6 when x = 4, and y = 10/3 when x = 3, then what is the relation between x and y?
    Answer

    According to the question

    y = lx + m/x …..(i)

    where l and m are proportionality constant.

    When y = 6 and 4, then

    6 = 4l + m/4

    Therefore, 16l + m = 24 …..(ii)

    When y = 10/3,  x = 3, then

    10/3 = 3l + m/3

    Therefore, 9l + m = 10

    On solving eqs. (ii) and (iii), we get

    l = 2 and m = -8

    from equation (i)

    y = 2x – 8/x

  • May 23 2017
    QuestionThe speed of a car increases by 2kmph by every hour. If the distance travelled in the first hour was 35 km, what was the total distance travelled in 12 hours?
    Answer

    This is the problem of Arithmetic Progression (A.P.) with a first term (a) =35
    common Difference (d) =2 and total number of terms (n) = 12.

    The sum of the distance will be calculated as

    Sum (Sn) =(n/2)[2a + (n – 1)d]

    = (12/2)[70 + 11*2] =6 x 92 =552

  • May 19 2017
    QuestionThe ratio of earning of A and B is 4 : 7 respectively. If the earning of A increases by 50% and the earning of B decreases by 25% the new ratio of their earnings becomes 8:7 respectively, what are the A’s earning?
    Answer

    Let the earning of A and B be 4x and 7x respectively

    New earning will be 6x and 7x – (7x/4) i.e. 6x and 21x/4

    Now by conditions

    (6x/21x/4) =8/7

    Or 8/7 = 8/7

    Thus, by the data, A’s earning cannot be determined as such

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