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Q.

A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/ hr from its usual speed. The usual speed of the train is [[1]].

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answer is 25 KM/HR.

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Detailed Solution

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A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/ hr from its usual speed. The usual speed of the train is 25 km/hr.
Given that a passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/ hr from its usual speed.
Let the usual speed of the train be

s km / hr

. Then time taken for the usual speed be,
Time

= \frac{300}{s}

If the speed is increased by 5 km/ hr then time required for the train when increased by 5 km/ hr from its usual speed will be,
Time

= \frac{300}{s + 5}

According to question,

⟹ \frac{300}{s} - \frac{300}{s + 5} = 2

⟹ \frac{300 (s + 5) - 300 s}{s (s + 5)} = 2

⟹ \frac{300 s + 1500 - 300 s}{s^{2} + 5 s} = 2

⟹ \frac{1500}{s^{2} + 5 s} = 2

⟹ 2 (s^{2} + 5 s) = 1500

⟹ s^{2} + 5 s = \frac{1500}{2}

⟹ s^{2} + 5 s = 750

⟹ s^{2} + 5 s - 750 = 0

⟹ s^{2} + 30 s - 25 s - 750 = 0

⟹ s (s + 30) - 25 (s + 30) = 0

⟹ s + 30 = 0 or s - 25 = 0

∴ s = - 30 or s = 25

s = - 30

is not possible due to negative sign.
Therefore, the usual speed of the train is 25 km/hr.

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A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/ hr from its usual speed. The usual speed of the train is [[1]].