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Research Aptitude Test - 6

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Research Aptitude Test - 6
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Weekly Quiz Competition
  • Question 1
    2 / -0.5

    Sashi can do a piece of work in 25 days and Rishi can do it in 20 days. They work for 5 days, then Sashi goes away. In how many more days will Rishi finish the work?

    Solution

    Shashi ’s one day work = 1/25

    Rishi ’s one day work = 1/20

    Together they can finish 1/25 + 1/20 = 9/100 part in a day

    ∴Work in 5 days (9/100)x5 = 45/100 part

    55/100 part is remaining. Rishi can finish it in (55/100)/(1/20) = 11 days.

  • Question 2
    2 / -0.5

    Manoj takes twice as much time as Ajay and thrice as much as Vijay to finish a piece of work. Together they finish the work in 1 day. What is the time taken by Manoj to finish the work?

    Solution

    Let Manoj takes 6x days Ajay takes 3x days and vijay 2x days then 1/6x + 1/3x + 1/2x = 1

    1/x [⅙ + ⅓ + ½ ] = 1

    1/x = 1, So x = 1

    Manoj will take 6 days.

  • Question 3
    2 / -0.5

    Raju works twice as Vijay. Together, they finish the work in 14 days, in how many days can Vijay alone do the same work?

    Solution

    Let Raju can do the work in x days then Vijay in 2x days

    Together they can complete in

    x = 21 days, 2x = 42 days

  • Question 4
    2 / -0.5

    What is the rate of simple interest for the first 4 years if the sum of Rs. 360 becomes Rs. 540 in 9 years and the rate of interest for the last 5 years is 6%?

    Solution

    P = Rs. 360, A = Rs. 540, SI = Rs. 180.

    SI = PRT/100

  • Question 5
    2 / -0.5

    A jay borrows Rs. 1500 from two money-lenders. He pays interest at the rate of 12% per annum for one loan and at the rate of 14% per annum for the other. The total interest he pays for the entire year is Rs. 186. How much does he borrow at the rate of 12%?

    Solution

    P = 1500, R1 = 12%, Rε = 14%, T = 1 year SI = 186

    Let Rs. x be amount invested at 12% Rate

  • Question 6
    2 / -0.5

    Two equal sums were borrowed at 8% simple interest per annum for 2 years and 3 years respectively. The difference in the interest was Rs. 56. The sum borrowed were

    Solution

  • Question 7
    2 / -0.5

    Sanjay borrowed Rs. 900 at 4% p.a. and Rs. 1100 at 5% p.a. for the same duration. He had to pay Rs. 364 in all as interest. What is the time period in years?

    Solution

    36T + 55T = 364

    T = 4 years

  • Question 8
    2 / -0.5

    A train 150 m long moving at a speed of 25 metres per second overtakes a man moving at 5 metres/sec in opposite direction.The train will pass the man in

    Solution

    Speed of train relative to man

    = (25 + 5) m/sec

    = 30 m/sec

    ∴ Time taken to pass the man

    = (150/30)sec = 5 sec.

  • Question 9
    2 / -0.5

    Two Train 126 m and 114 m long are running in opposite directions, one at the rate of 30 kmph and another one at 42 kmph. From the moment they meet will cross each other in

    Solution

    Relative speed = (30+42) kmph = 72 kmph

    = (72 x (5/18))m/sec = 20 m/sec

    Distance covered in crossing each other = (126 + 114) m = 240 m.

    Required time = (240/20)sec= 12 sec.

  • Question 10
    2 / -0.5

    A train 110m long passes a man, running at 6 kmph in the direction opposite to that of the train, in 6 seconds. The speed of the train is

    Solution

    Speed of the train relative to man = (110/6) m/sec. =

    = 66 kmph.

    Let the speed of the train be x kmph.

    Then, relative speed = (x + 6) kmph.

    x + 6 = 66 or x = 60 kmph.

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