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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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