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Overtaking Time for Three Travelers

CAT 2006 Slot 1 · Quantitative Ability · Medium · Quantitative Aptitude

This is a medium Quantitative Ability question from the CAT 2006 Slot 1 paper. It tests Quantitative Aptitude. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40 and 60 km per hour respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

  1. A.

    3

  2. B.

    3.5

  3. C.

    4

  4. D.

    4.5

  5. E.

    5

Answer

Option D — 4.5

Explanation

Let Arun start at t=0t = 0. In 2 hours, Arun travels 30×2=6030 \times 2 = 60 km. Relative speed of Barun w.r.t Arun =40−30=10= 40 - 30 = 10 km/h. Time taken by Barun to overtake Arun =60/10=6= 60 / 10 = 6 hours after Barun starts. So Barun overtakes Arun at t=2+6=8t = 2 + 6 = 8 hours after Arun started. At t=8t = 8 hours, distance traveled by Arun =30×8=240= 30 \times 8 = 240 km. Kiranmala also overtakes Arun at t=8t = 8 hours. Since Kiranmala's speed is 60 km/h, time taken by Kiranmala =240/60=4= 240 / 60 = 4 hours. So Kiranmala started 8−4=48 - 4 = 4 hours after Arun.

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