Races and games


  1. In a race of 300 meter, A beats B by 15 meter or 5 sec. A’s time over the course is :
    1. 100 seconds
    2. 95 seconds
    3. 105 seconds
    4. 90 seconds

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    15 meter is covered by B in 5 sec .
    ∴ 300 meter is covered by B in 5 × 300/15 = 100 seconds

    Correct Option: B

    15 meter is covered by B in 5 sec
    ∴ 300 meter is covered by B in 5 × 300/15 = 100 seconds
    A takes 100 - 5 = 95 seconds.


  1. A runs 138 times as fast as B. If A gives B a start of 120 m and they reach the goal at the same time, the goal is at a distance of:
    1. 360 m
    2. 440 m
    3. 460 m
    4. 380 m

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    The speed of A and B are in the ratio 11 : 8.
    Let, speeds be 11s and 8s (in m/sec).
    Let, race be of P meter.

    Correct Option: B

    The speed of A and B are in the ratio 11 : 8.
    Let, speeds be 11s and 8s (in m/sec).
    Let, race be of P meter.
    Then, time taken by A to run P meter is same as that of B to run (P - 120) meter.
    ∴ P / 11 = (P - 120) / 8
    ∴ P / 11 = (P - 120 / 8
    ∴ 8P = 11 x (P - 120 )
    ∴ 8P = 11P - 120 x 11
    ∴ 11P - 8P = 120 x 11
    ∴ 3P = 11 × 120
    ∴ P = 440.



  1. At a game of billiards, A can give B 6 points in 50 and he can give C 13 in 65. In a game of 55, number of points B can give C is:
    1. 3
    2. 4
    3. 5
    4. 8

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    In a game of 50.
    While A scores 50, B scores 50 - 6 = 44 and in a game of 65. While A scores 65, C scores 65 - 13 = 52.

    Correct Option: C

    In a game of 50.
    While A scores 50, B scores 50 - 6 = 44 and in a game of 65. While A scores 65, C scores 65 - 13 = 52.
    ∴ While A scores 50, C scores 52 / 65 × 50 = 40.
    ∴ While B scores 44, C’s score = 40.
    While B scores 55, C’s score = 40 / 44 × 55 = 50.
    ∴ In a game of 55,
    B can give C 55 - 50 = 5 points.