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City Bus Corporation Meeting Buses

XAT 2012 · Quantitative Ability & Data Interpretation · Hard · Time Speed and Distance

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City Bus Corporation runs two buses from terminus A to terminus B, one from each of the terminuses such that each bus makes 5 round trips in a day. There are no stops in between. These buses ply back and forth on the same route at different but uniform speeds. Each morning the buses start at 7 AM from the respective terminuses. They meet for the first time at a distance of 7 km from terminus A. Their next meeting is at a distance of 4 km from terminus B, while travelling in opposite directions. Assuming that the time taken by the buses at the terminuses is negligibly small, and the cost of running a bus is 20 per km, find the daily cost of running the buses (in rupees)

  1. A.

    3200

  2. B.

    6800

  3. C.

    4000

  4. D.

    6400

  5. E.

    None of the above

Answer

B

Explanation

Let total distance between A and B be PP. First meeting: distance covered by bus A = 7, total combined distance = PP. Second meeting: total combined distance = 3P3P, distance covered by bus A = P+4P + 4. Since speed ratio is constant: P+47=3PP=3  ⟹  P+4=21  ⟹  P=17\frac{P+4}{7} = \frac{3P}{P} = 3 \implies P + 4 = 21 \implies P = 17 km. Each round trip = 2×17=342 \times 17 = 34 km. 5 round trips per bus = 5×34=1705 \times 34 = 170 km. Total distance for 2 buses = 2×170=3402 \times 170 = 340 km. Total daily cost = 340×20=Rs. 6800340 \times 20 = \text{Rs. } 6800.

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