Quantitative Aptitude – Proportion – One third of the buses from City

XAT 2021 Exam Paper – Quantitative Aptitude – Proportion – One third of the buses from City

Q. 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. 1/7
2. 1/3
3. 4/9
4. 7/9
5. 1/9

Solutions:
lets say there are x buses that goes from city A to city B vaya city C.
As per question, x/3 of them stop at C and 2x/3 go on-stop to B.
It is also given that one-third of the passengers, in the buses stopping at City C, continue to City B, while the rest alight at City C Since all buses have equal capacity. we can say 2/3 (x/3) = 2x/9 will stop at C and x/9 will proceed to B.
Thus required ratio = (x/9)/(2x/3+x/9) = x/7x = 1/7
Hence required proportion = 1/7

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