Two trains start at the same time from stations P and Q and travel towards each other at the speeds of 75 km/h and 100 km/h, respectively. When they meet, it is found that one train has travelled 50 km more than the other. The distance (in km) between two stations is:

Question

Question

This question was previously asked in

SSC Selection Post 2024 (Matriculation Level) Official Paper (Held On: 25 Jun, 2024 Shift 1)

Answer 1

Given:

Speed of train from P = 75 km/h

Speed of train from Q = 100 km/h

One train has travelled 50 km more than the other

Formula used:

Let the distance travelled by the train from P be x km

Then, the distance travelled by the train from Q = x + 50 km

Time taken to meet is the same for both trains

Time = Distance / Speed

Calculation:

Time taken by train from P = x / 75

Time taken by train from Q = (x + 50) / 100

Since the time taken is the same:

⇒ x / 75 = (x + 50) / 100

⇒ 100x = 75(x + 50)

⇒ 100x = 75x + 3750

⇒ 100x - 75x = 3750

⇒ 25x = 3750

⇒ x = 150

Total distance = Distance travelled by train from P + Distance travelled by train from Q

⇒ 150 + (150 + 50)

⇒ 150 + 200

⇒ 350 km

∴ The correct answer is option 2.

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