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    Question

    In a 400 metres race, 'X' defeats 'Z' by 80 metres and

    'Z' defeats 'Y' by 50 metres. By how many metres does 'X' beat 'Y'?
    A 120 m Correct Answer Incorrect Answer
    B 115 m Correct Answer Incorrect Answer
    C 125 m Correct Answer Incorrect Answer
    D 136 m Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the time taken by 'X' to complete the race = 't' seconds

    Distance run by 'X' in t seconds = 400 metres

    Distance run by 'Z' in 't' seconds = 400 - 80 = 320 metres

    So, the ratio of speeds of 'X' and 'Z' = 400 : 320 = 5 : 4

    Similarly, since 'Z' beats 'Y' by 50 metres:

    Ratio of speeds of 'Z' and 'Y' = 400 : (400 - 50) = 400 : 350 = 8 : 7

    Now, combine ratios to get:

    Ratio of speeds of 'X', 'Z', 'Y' = 5×8 : 4×8 : 4×7 = 40 : 32 : 28

    So, when 'X' finishes 400 metres, 'Y' covers = 400 × (28/40) = 280 metres

    Therefore, 'X' beats 'Y' by 400 - 280 = 120 metres

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