Question

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?

• A. 4/9
• B. 6/7
• C. 1/7
• D. 2/7
• E. 7/9

Hint:

Use a convenient number for buses (like 3) and capacity (like 1) to simplify calculations.

Answer 1

The Correct Option is C

Step 1: Let total number of buses = $3n$ (so that 1/3 is integer). Then buses stopping at C = $n$, non-stop = $2n$. Each bus capacity = $c$ passengers. Total passengers from A = $3nc$.
Step 2: Buses stopping at C: $n$ buses, each full with $c$ passengers. $1/3$ of these continue to B, so $\frac{nc}{3}$ continue. The rest ($\frac{2nc}{3}$) alight at C.
Step 3: Non-stop buses: $2n$ buses, all $2nc$ passengers go to B.
Step 4: Total passengers going to B = from non-stop ($2nc$) + from stopping buses ($\frac{nc}{3}$) = $2nc + \frac{nc}{3} = \frac{6nc + nc}{3} = \frac{7nc}{3}$.
Step 5: Proportion traveling by bus stopping at C = $\frac{nc/3}{7nc/3} = \frac{1}{7}$.
Step 6: Final Answer: 1/7.