Question

A bus starting from delhi is carrying a certain number of passengers. At the next stop agra 1/3rd of the total passengers alight and 18 new passengers get in. At the next stop kanpur, 3/4th of the remaining get down and 12 passengers get in, after which there are 25 passengers in the bus. How many passengers were there in the bus when it left delhi?

Answer 1

let the original no of passengers be x

no of passengers in the bus after leaving Agra
= x - x/3 + 18
=2x/3 + 18

No of passengers in the bus after leaving Kanpur = 3/4(2x/3 + 18) + 12
3/4(2x/3 + 18) = 25-12
2x/3+18 = 13*4/3
2x/3=52/3-18
2x/3=-2/3
x= -1

Answer 2

Let the total passengers be x.

At Agra the ones who alight = 1/3x

Remaining = 2/3x

When 18 more join them we have :

2/3x + 18

At the next stop the ones who alight = 3/4 × (2/3x + 18) = 1/2x + 13.5

Remaining = (2/3x + 18) - (1/2x + 13.5)

= 1/6x + 4.5

When 12 more join.

1/6x + 4.5 + 12

= 1/6x + 16.5

This equals to 25

1/6x + 16.5 = 25

x + 99 = 150

x = 150 - 99

x = 51

There were 51 passengers when the bus left Delhi