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Proportion of Passengers Stopping at City C

XAT 2021 · Quantitative Ability & Data Interpretation · Medium · Arithmetic

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One third of the buses from City A to City B stop at City C, while the rest go non-stop to City B. One third of the passengers, in the buses stopping at City C, continue to City B, while the rest alight at City C. All the buses have equal capacity and always start full from City A. What proportion of the passengers going to City B from City A travel by a bus stopping at City C?

  1. A.

    17\frac{1}{7}

  2. B.

    19\frac{1}{9}

  3. C.

    13\frac{1}{3}

  4. D.

    79\frac{7}{9}

  5. E.

    49\frac{4}{9}

Answer

A

Explanation

Let total buses from A to B = 3, each with capacity 30. Total passengers starting from A = 90. Non-stop buses to B = 2 buses = 60 passengers directly to B. Stopping buses at C = 1 bus = 30 passengers. Of these 30 passengers, 1/3 continue to B = 10 passengers; 2/3 alight at C = 20 passengers. Total passengers reaching City B = 60 (from non-stop) + 10 (from stopping) = 70. Passengers going to B who traveled on stopping bus = 10. Required proportion = 1070=17\frac{10}{70} = \frac{1}{7}.

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