Question

A train starts full of passengers. at the first station it drops 1/3 of the passengers and takes 280 more at the second station it drops one half the new total and takes twelve more. on arriving at the third station it is found to have 248 passengers. find the no. of passengers in the beginning?

Answer 1

at the beginning no . of passengers was 144

Answer 2

Let the number of passengers in the beginning be x.

On arriving 2nd station, number of passengers is
$\frac{2}{3} x + 280$

On arriving 3rd station, number of passengers is
$\frac{1}{2} \times ( \frac{2}{3} x + 280) + 12 \\ = \frac{x}{3} + 152$

Given,
$\frac{x}{3} + 152 = 248 \\ x = 3 \times 96 = 288$