Question

A bus starts from its depot filled to the seating capacity. It stops at a point A where 1/6^th of the passengers alight and 10 boards of the bus. At point B, 1/5^th 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
1. 96
2. 99
3. 66
4. 90

Answer 1

Correct Answer - Option 3 : 66

Given:

At point A, 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.

Calculations:

Let total number of passenger be x.

At point A,1/6th 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, 1/5th 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.