Races and games


  1. In a race of 600 m, A can beat B by 30 m and in a race of 500 m, B can beat C by 25 m. By how many metres will A beat C in a race of of 400 m ?
    1. 39 m
    2. 49 m
    3. 55 m
    4. 25 m

  1. View Hint View Answer Discuss in Forum

    If A runs 600 m, then B runs 570 m.
    If A runs 400 m, B then runs (570/600) x 400 m = 380 m
    When B runs 500 m, then C runs 475 m,
    When B runs 380 m, then C runs (475/500) x 380 = 361 m

    Correct Option: A

    If A runs 600 m, then B runs 570 m.
    If A runs 400 m, B then runs (570/600) x 400 m = 380 m
    When B runs 500 m, then C runs 475 m,
    When B runs 380 m, then C runs (475/500) x 380 = 361 m
    ∴ A beats C by (400 - 361) = 39 m


  1. A runs 1% times as fast as B. If A gives B a start of 30 m, how far must the winning post be, so that A and B reach it at the same time ?
    1. 52 m
    2. 75 m
    3. 69 m
    4. 70 m

  1. View Hint View Answer Discuss in Forum

    A is 13/4 faster than B.
    Then, ratio of the rates of A and B = 7 : 4
    3 m are gained in a race of 7 m .
    30 m are gained in a race of (7/3) x 30 = 70 m

    Correct Option: D

    A is 13/4 faster than B.
    Then, ratio of the rates of A and B = 7 : 4
    3 m are gained in a race of 7 m .
    30 m are gained in a race of (7/3) x 30 = 70 m



  1. In a 250 m race, the ratio of speeds of A and B is 1 : 2, If A has a start of 140 m, then A wins by how many metres ?
    1. 45 m
    2. 15 m
    3. 25 m
    4. 30 m

  1. View Hint View Answer Discuss in Forum

    To reach the winning post, A has to cover (250 - 140)m = 110 m
    From the the ratio of 1 : 2 ,
    When A covers 1m, then B covers 2 m

    Correct Option: D

    To reach the winning post, A has to cover (250 - 140)m = 110 m
    From the the ratio of 1 : 2 ,
    When A covers 1m, then B covers 2 m.
    When A covers 110 m, then B covers
    ( 2 x 110)m = 220 m
    ∴ A wins by (250 - 220) = 30 m


  1. In 1 km race, P beats Q by 72 m in 12 s. Find the P's time over the course.
    1. 1552/3 s
    2. 151 s
    3. 1542/3 s
    4. 160 s

  1. View Hint View Answer Discuss in Forum

    According to the formula,
    Time taken by the winner/Distance covered by the loser = Difference of winning time/ Difference of winning distance
    ⇒ Time taken by P//(1000 - 72) = 12/72

    Correct Option: C

    According to the formula,
    Time taken by the winner/Distance covered by the loser = Difference of winning time/ Difference of winning distance
    ⇒ Time taken by P//(1000 - 72) = 12/72
    ∴ Time taken by P = (12/72) x 928
    = 464/3 = 1542/3 s



  1. X covers 1 km in 8 min 40 s while Y covers the same distance in 10 min. By what distance does X defeat Y?
    1. 131/3 m
    2. 1332/3 m
    3. 1332/5 m
    4. 1331/3 m

  1. View Hint View Answer Discuss in Forum

    Clearly, X beats Y by 8 s.
    Distance covered by Y in 600 s = 1000 m

    Correct Option: D

    Clearly, X beats Y by 8 s.
    Distance covered by Y in 600 s = 1000 m
    (∵ 10 min = 600 s)
    Distance covered by Y 80 s. = (1000/600) x 80 = 400/3 m = 1331/3 m