Question

Two trains are running in opposite directions. They cross a man standing on a platform in 28 seconds and 10 seconds. respectively. They cross each other in 24 seconds. What is the ratio of their speeds?

• A. 7 : 2
• B. 1 : 9
• C. 9 : 2
• D. 4 : 5

Answer 1

Answer:

A. 7 : 2

Shortcut Trick

We can solve this question by applying the allegation method.

Thus,

Ratio of their speed = 14 : 4 = 7 : 2

∴ The correct answer is option (1).

Alternate Method

Given:

Train one crosses a man in 28 seconds

Train two crosses the man in 10 seconds

They both cross each other in 24 seconds

Formula used:

Time = Distance/ speed

As the trains travel in opposite directions, the speed of the trains added

Calculation:

Let the speed of the first train & second train be x m/s and y m/s respectively.

Length of the first train is 28x metres

Length of the second train is 10y meters

According to the question,

⇒ 24 = (28x + 10y) / (x + y)

⇒ 24x + 24y = 28x + 10y

⇒ 14y = 4x

⇒ x/y = 7/2

∴ The ratio of the speed of the train is 7 : 2.