Let the number of passenger in train(when train started from mumbai) $ = x$
From second station: The number of passenager $ = x – \dfrac{x}{3} + 96 = \dfrac{2x + 288}{3}$
From second station: The number of passenager $ = \dfrac{2x + 288}{3} – \left(\dfrac{ \dfrac{2x + 288}{3} }{2}\right) + 12$
Now, $\dfrac{2x + 288}{3} – \left(\dfrac{ \dfrac{2x + 288}{3} }{2}\right) + 12 = 248$
$\implies \dfrac{2x + 288}{3} – \left(\dfrac{x + 144}{3}\right) + 12 = 248$
$\implies \dfrac{2x + 288 – x – 144 + 36}{3} = 248$
$\implies x + 180 = 744$
$\implies x = 564.$
So, the correct answer is $(B).$