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    Question

    'R' started his journey from point 'X' towards point 'Y' at

    40 km/h. Three hours later, 'S' left point 'X' towards point 'Y' at 70 km/h. 'T' left point 'X' towards 'Y' after 'M' hours of 'R's journey at 105 km/h. If both 'S' and 'T' overtook 'R' at the same time, find the value of M.
    A 4.33 Correct Answer Incorrect Answer
    B 8.88 Correct Answer Incorrect Answer
    C 12.11 Correct Answer Incorrect Answer
    D 17.33 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Distance covered by 'R' in the first three hours = 40 × 3 = 120 km

    Relative speed of 'S' with respect to 'R' = 70 − 40 = 30 km/h

    Time taken by 'S' to overtake 'R' = 120 ÷ 30 = 4 hours

    Distance covered by 'S' in 4 hours = 70 × 4 = 280 km

    Time taken by 'T' to cover 280 km = 280 ÷ 105 = 2.67 hours

    So, 'T' must have left 2.67 hours before 'S' overtook 'R', i.e., 4 − 2.67 = 1.33 hours after 'S' left

    Therefore, M = 3 + 1.33 = 4.33 hours

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