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MAT Exam 2024 Paper

Question : 76 of 150

Marks: +1, -0

A man sitting in a train travelling at the rate of

60 \mathrm{~km} / \mathrm{hr}

observes that it takes 18 sec for a goods train travelling in the opposite direction to pass him. If the goods train is 375 m long, find its speed.

25 km/hr
40 km/hr
15 km/hr
36 km/hr

Validate

Solution:

Concept:

When two trains move in opposite directions, their relative speed is the sum of their speeds. The time taken to pass a person equals the train’s length divided by this relative speed.

Explanation:

Speed of the man’s train is

60 \ \mathrm{km/hr} = 60 \times \frac{5}{18} = \frac{50}{3} \ \mathrm{m/s}

Let the speed of the goods train be

x \ \mathrm{m/s}

Relative speed

= x + \frac{50}{3}

Using Distance

=

Relative speed

\times

Time:

375 = \left(x + \frac{50}{3}\right) \times 18

375 = 18x + 300

18x = 75

x = 4.16\ \mathrm{m/s}

Convert to km/hr:

4.16 \times \frac{18}{5} = 15 \ \mathrm{km/hr}

Answer:

15 \ \mathrm{km/hr}

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