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Select the correct answerA train covers a certain distance in 45 minutes. If its speed is reduced by 5 km/h, it takes 3 minutes more to cover the same distance. The distance (in km) is?Options₹ 60₹ 64₹ 54₹ 80

Question

Select the correct answerA train covers a certain distance in 45 minutes. If its speed is reduced by 5 km/h, it takes 3 minutes more to cover the same distance. The distance (in km) is?Options₹ 60₹ 64₹ 54₹ 80

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Solution

The problem can be solved using the concept of relative speed.

Let's denote the original speed of the train as 's' (in km/h) and the distance it covers as 'd' (in km).

According to the problem, the train covers this distance 'd' in 45 minutes or 45/60 = 0.75 hours. So, we can write the first equation from the formula of speed = distance/time as:

s = d / 0.75 ----(1)

The problem also states that if the speed of the train is reduced by 5 km/h, it takes 3 minutes more to cover the same distance. So, the speed becomes (s-5) km/h and the time becomes (45+3) = 48 minutes or 48/60 = 0.8 hours. We can write the second equation as:

s - 5 = d / 0.8 ----(2)

Now, we have a system of two equations (1 and 2). We can solve this system to find the values of 's' and 'd'.

Subtracting equation (2) from equation (1), we get:

5 = d/0.75 - d/0.8

Solving this equation for 'd', we get:

d = 60 km

So, the correct answer is ₹ 60.

This problem has been solved

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