Question 22

A train starts full of passengers. At the first station, it drops one third of passengers and takes 280 more. At the second station, it drops one half of the new total and takes 12 more. On arriving at the third station, it is found to have 248 passengers. The number of passengers in the beginning was

Solution

Let the no of passengers at start be "N" .

At first station it drops 1/3rd and takes 280 more :
Now the passengers = $$N(1-\dfrac{\ 1}{3})+280$$ = 2N/3 + 280.

At second station, it drops 1/2 part of new total and takes 12 more :
Now the passengers count after 2nd station will be = N/3 + 140 + 12 = N/3 + 152.

It is given that this value {N/3 + 152} = 248.
So, N = 96(3) = 288

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