Races and games


  1. A and B run a 5 Km race on a round course of 400 m. If their speeds be in the ratio 5 : 4, then how often does the winner pass the other?









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    When A makes 5 rounds, B makes 4 rounds.
    In order to pass each other, the difference in number of rounds made by each must be one.
    Here, A passes B each time, when A makes 5 rounds.
    Distance covered by A in 5 rounds = 5 * 400 / 100 × = 2 Km.

    Correct Option: D

    When A makes 5 rounds, B makes 4 rounds.
    In order to pass each other, the difference in number of rounds made by each must be one.
    Here, A passes B each time, when A makes 5 rounds.
    Distance covered by A in 5 rounds = 5 * 400 / 100 × = 2 Km.
    In covering 2 Km, A passes B 1 time.
    ∴ In covering 5 Km, A passes B
    = 5 / 2 = 212 times.


  1. In a game of 100 points, A can give B 20 points and C 28 points. Number of points B can give C in a game of 100 points is:









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    A scores 100 while B scores 100 - 20 = 80 and C scores 100 - 28 = 72.
    ∴ While B scores 80, C scores 72.

    Correct Option: A

    A scores 100 while B scores 100 - 20 = 80 and C scores 100 - 28 = 72.
    ∴ While B scores 80, C scores 72.
    ∴ While B scores 100, C scores 72 × 100 / 80 = 90.
    ∴ B can give C 100 - 90 = 10 points.



  1. The respective ratio between the speeds of a car, a train and a bus is 5 : 9 : 4. The average speed of the car, the bus and the train is 72 Km/h together. What is the average speed of the car and the train together?









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    Total speed of car, bus and train = 72 × 3 = 216 Km
    Speed of car and train = ( 5 + 9 ) x 216 / ( 5 + 9 + 4 ) = 168 Km

    Correct Option: C

    Total speed of car, bus and train = 72 × 3 = 216 Km
    Speed of car and train = ( 5 + 9 ) x 216 / ( 5 + 9 + 4 ) = 168 Km
    Average = 168 / 2 = 84 Km


  1. In a game of 90 points, A can give B 15 points and C 30 points. How many points can B give C in a game of 100 points?









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    A:B:C = 90:75:60
    B : C = 75 / 60 = ( 75 x 10075 ) / ( 60 x 10075) = 100 / 80

    Correct Option: B

    A : B : C = 90 : 75 : 60
    B:C = 75 / 60 = ( 75 x 10075 ) / ( 60 x 10075) = 100 / 80
    Hence, in a game of 100 points, B can give C(100 - 80)
    = 20 points.



  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?









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    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