Races and games

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  1. A can beat B by 5 meters in 100 m and B can beat C by 15 meters in 200 m race. A can beat C in 400 m race by:
    1. 50.5 m
    2. 48.5 m
    3. 45.5 m
    4. 42.5 m

  1. View Hint View Answer Discuss in Forum

    ∴ A runs 100 m while B runs 95 m
    ∴ A runs 400 m while B runs 95 x 400 / 100 = 380 m

    Correct Option: B

    ∴ A runs 100 m while B runs 95 m
    ∴ A runs 400 m while B runs 95 x 400 / 100 = 380 m

    Again, B runs 200 m while C runs 185 m
    ∴ B runs 380 m while C runs 185 x 200 / 380 = 3515 / 10 = 351.5 m

    Hence, A runs 400 m while C runs 351.5 m
    So, A can beat C by (400 – 351.5) = 48.5 m

  1. At a game of billiards A can give B 6 points in 50 and he can give C 13 points in 65, how many points can B give C in a game of 55?
    1. 7
    2. 8
    3. 5
    4. 10

  1. View Hint View Answer Discuss in Forum

    In a game of 50, If A scores 50 then B scores 44.

    ∴ A scores 65 while B 44 * 65 / 50 = 57.2 points

    Correct Option: C

    In a game of 50, If A scores 50 then B scores 44.
    ∴ A scores 65 while B 44 * 65 / 50 = 57.2 points
    Now, B scores 57.2 points while C 52
    ∴ B scores 55 points while C = 52 * 55 / 57.2 = 50
    Hence, in game of 55 points B can give C (55 – 50) = 5 points

  1. In a race of 200 metres, B can give a start of 10 metres to A and C can give a start of 20 metres to B. The start that C can give to A, in the same race, is
    1. 30 m
    2. 29 m
    3. 27 m
    4. 25 m

  1. View Hint View Answer Discuss in Forum

    B covers 200 m while A 190 m
    B covers 180 m while A 190 / 200 * 180 = 171 m

    Correct Option: B

    B covers 200 m while A 190 m
    B covers 180 m while A 190 x 180 / 200 = 171 m
    Hence, C covers 200 m while A = 171 m
    So, C can give to A (200 – 171) = 29 m start.

  1. A can run 500m in 30 seconds and B in 35 seconds. How many meter start can A give to B in a Km race so that the race may end in a dead-heat?
    1. 1395⁄7
    2. 1385⁄7
    3. 1426⁄7
    4. 1405⁄7

  1. View Hint View Answer Discuss in Forum

    Time taken by A to run 1 Km = 30 × 2 = 60 seconds.
    Time taken by B to run 1 Km = 35 × 2 = 70 seconds.
    ∴ A can give B a start of (70 - 60) = 10 seconds.

    Correct Option: C

    Time taken by A to run 1 Km = 30 × 2 = 60 seconds.
    Time taken by B to run 1 Km = 35 × 2 = 70 seconds.
    ∴ A can give B a start of (70 - 60) = 10 seconds.
    In 35 sec B runs 500 m
    ∴ In 10 sec B runs = 500 × 10 / 35 = 1000 / 7 = 1426⁄7 meters
    So, A can give B a start of 1426⁄7 meters in a Km race.

  1. A’s speed is 13⁄8 times of B’s. In a race A gives B a start of 300 m. How long should the race course be so that both reach the winning post simultaneously?
    1. 700 m
    2. 900 m
    3. 800 m
    4. 850 m

  1. View Hint View Answer Discuss in Forum

    A’s speed : B’s speed = 11⁄2 : 1
    = 3⁄2 : 1
    = 3 : 2
    It means that in a race of 3 m, A gains (3 - 2).
    = 1 m over B. 1 m is gained by A in a race of 3 m.

    Correct Option: B

    A’s speed : B’s speed = 11⁄2 : 1
    = 3⁄2 : 1
    = 3 : 2
    It means that in a race of 3 m, A gains (3 - 2).
    = 1 m over B. 1 m is gained by A in a race of 3 m.
    ∴ 300 m is gained by A in a race of = 3⁄1 × 300 = 900 m.