A bus starts from its depot filled to the seating capacity. It stops at a point A where 1/6th of the passengers alight and 10 boards of the bus. At point B, 1/5th of the passengers alight and 3 boards the bus. At point C which is the last stop, all the 55 passengers alight. The capacity of the bus is
Explanation
Given:
At point A, 1/6 of the passengers alight and 10 boards of the bus.
At point B, 1/5 of the passengers alight and 3 boards the bus.
At point C which is the last stop, all the 55 passengers alight.
Calculations:
Let total number of passenger be x.
At point A,1/6 of the passengers alight and 10 boards of the bus,
Number of passengers in the bus = x - x/6 + 10
⇒ 5x/6 + 10
At point B, 1/5 of the passengers alight and 3 boards the bus,
Now, Number of passengers in the bus = (5x/6 + 10) - {(1/5)(5x/6 + 10)} + 3
⇒ (5x/6 + 10)(1 - 1/5) + 3
⇒ (5x/6 + 10)(4/5) + 3
⇒ (4x/6 + 8) + 3
⇒ 4x/6 + 11
⇒ 2x/3 + 11
At point C, 55 passengers alight the bus,
⇒ 2x/3 + 11 = 55
⇒ 2x/3 = 44
⇒ x = 132/2
⇒ x = 66
∴ The capacity of the bus is 66.
