A train starts with full number of passengers. At the first stop, it drops one third of the passengers and takes in 96 more. At the second stop, it drops one half of the passengers onboard and takes in 12 more. If there are 248 passengers onboard traveling to third station, then with how many passengers did the train start?

Correct option is A

​​Given:

Number of passengers onboard traveling to the third station = 248

Formula Used:

Number of passengers at the second stop = Number of passengers onboard traveling to the third station × 2

Solution:

After 2nd stop:

=> Before +12, passengers = 248 - 12 = 236

As 236 is half the passengers after 1st stop,

=> Passengers after 1st stop = 236 × 2 = 472

Passengers after 1st stop:

=> $$\frac{2}3$$​ × original + 96 = 472

Solving for original:

=> $$\frac{2}3$$​ × original = 472 - 96 = 376

=> original = 376 × $$\frac{3}2$$​ = 564