The ratio of lengths of trains A and B is 5 : 3 and the ratio of their speeds is 2 : 3. Moving in the opposite direction, it took \(2\frac{1}{2}\) minutes for Train A to cross B. The time (in minutes) taken by A to cross a stationary pole is:

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SSC MTS Previous Paper 36 (Held On: 21 August 2019 Shift 3)
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  1. 2
  2. 3
  3. \(\frac{{125}}{{32}}\)
  4. \(\frac{{25}}{{16}}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{{125}}{{32}}\)
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Detailed Solution

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Given:

The ratio of lengths of trains A and B is 5 : 3

The ratio of their speeds is 2 : 3

Time taken to cross each other =  \(2\frac{1}{2}\) minutes = 5/2 minutes

Formula used:

Time = Distance/Speed

Calculation:

Let the Lengths od train A and B be 5x and 3x respectively

And Speed of A and B be 2y and 3y respectively

⇒ (5x +3x)/(2y + 3y) = 5/2

⇒ x/y = 25/16

Take x = 25 and y = 16

Now,

Length of Train A = 5x = 5 × 25 = 125

Speed of Train A = 2y = 2 × 16 = 32

∴ The time (in minutes) taken by A to cross a stationary pole = 125/32 Minutes

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