A bus starts from its depot filled to seating capacity. It stops at a point A where 1/6th of the passengers alight and 10 board the bus. At point B, 1/5th of the passengers alight and 3 board the bus. At point C which is the last stop, all the 55 passengers alight. The capacity of the bus is

Let the number of children = n

Total sweets = 405

Each child gets = \( \frac{405}{n} \) sweets

Given: Each child’s sweets = \( \tfrac{1}{5} \) of the number of children

⇒ \( \frac{405}{n} = \frac{n}{5} \)

Cross multiply:

\( 405 \times 5 = n^2 \)
⇒ \( n^2 = 2025 \)
⇒ \( n = \sqrt{2025} = 45 \)

✅ Final Answer: The number of children = 45