A bus starts from its depot filled to the seating capacity. It stops at a point A where 1/6<sup>th</sup> of the passengers alight and 10 boards of the bus. At point B, 1/5<sup>th</sup> 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
Step-by-step Solution:
The easiest way to solve this problem is to start from the final number of passengers at the last stop (C) and work backwards to find the initial number at the depot.
We know that all 55 passengers alight at stop C. This means just before arriving at C, there were 55 people on the bus.
Let 'x' be the number of passengers before the bus stopped at B. At the stop, 1/5th of the passengers alighted (leaving 4/5ths on board) and then 3 boarded. This resulted in the 55 passengers who were on the bus before stop C.
(x * 4/5) + 3 = 55 x * 4/5 = 52 x = (52 * 5) / 4 = 65 So, there were 65 passengers on the bus just before it reached stop B.
Let 'y' be the number of passengers before the bus stopped at A. At this stop, 1/6th alighted (leaving 5/6ths on board) and then 10 boarded. This resulted in the 65 passengers who were on the bus before stop B.
(y * 5/6) + 10 = 65 y * 5/6 = 55 y = (55 * 6) / 5 = 66 So, there were 66 passengers on the bus just before it reached stop A.
The problem states the bus started from the depot "filled to the seating capacity." The number of people on the bus when it started its journey was 'y'.
Final Answer: The capacity of the bus is 66.