Question 70

A train is to cover 370 km at a uniform speed. After running 100 km,the train could run at a speed 5 km/h less than its normal speed due to some technical fault. The train got delayed by 36 minutes. What is the normal speed of the train, in km/h?

Solution

Let the normal speed of the train = s km/h

According to the problem,

$$\frac{100}{s}+\frac{270}{s-5}=\frac{370}{s}+\frac{36}{60}$$

$$\frac{270}{s-5}-\frac{270}{s}=\frac{3}{5}$$

$$90\left[\frac{s-s+5}{\left(s-5\right)s}=\frac{1}{5}\right]$$

$$s^2-5s-2250=0$$

s = 50 or s = -45

's' cannot be negative.

So s = 50 km/h

Normal speed of the train = s = 50 km/h

Hence, the correct answer is Option D

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