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A train starts with some passengers. At the first stop, one-third of the passengers got down and 60 people got in. At the second stop, half of the passengers got down and 120 people got in. Then, the train left for its stopping place with 330 passengers. The number of passengers with which the train started was

A train starts with some passengers. At the first stop, one-third of the passengers got down and 60 people got in. At the second stop, half of the passengers got down and 120 people got in. Then, the train left for its stopping place with 330 passengers. The number of passengers with which the train started was Correct Answer 540

Given:

At the first stop, people got in = 60

At the second stop, people got in = 120

The train left for its stopping place with passengers = 330 

Calculation:

Let the number of passengers in the starting be P

According to the question

Number of passengers after first stop = + 60

⇒

Number of passengers after second stop = (1/2) ×  + 120      ----(1)

But, number of passengers after second stop = 330      ----(2)

From equation (1) and (2), we have

(1/2) ×  + 120 = 330

⇒ (1/2) ×  = 210

⇒ (2P/3) + 60 = 210 × 2

⇒ 2P/3 = 360

⇒ P = (360 × 3)/2

⇒ P = 540

∴ The number of passengers on the train when it started was 540.

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