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    Question

    A cyclist travelling at three-fourths of his usual speed

    takes 12 minutes longer than his usual time to cover a certain distance. Calculate the usual time taken by him.
    A 19 min Correct Answer Incorrect Answer
    B 12 min Correct Answer Incorrect Answer
    C 18 min Correct Answer Incorrect Answer
    D 27 min Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the usual speed of the cyclist be '4s' km/h and the distance travelled be 'd' km.

    Let the usual time taken by the cyclist to reach his destination be 't' hours.

    ATQ;

    (d/4s) = t

    Or, d = 4ts ........ (I)

    Now, if he travels at three-fourths of his speed:

    (d/(3s)) = t + (12/60)

    Using equation (I), we have;

    (4ts/3s) = t + (1/5)

    Or, 4t = 3t + (1/5)

    Or, t = (1/5)

    Thus, the usual time taken by the cyclist to reach his destination = (1/5) hours or 12 minutes.

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