1.

A train travels 360 km at a uniform speed.If the speed had been 5km/h more, it would have taken 1 hour less for the same journey.Find the speed of the train.

Answer»

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Assumption

Original speed of train :-

= p km/h

Also,

TIME TAKEN to cover 360 km

= 360/p hours

So,

Time taken to cover 360 km (Combined) :-

= 360/p + 5 hr

Situation :-

⇒ 360/p - 360/p + 5 = 1

⇒ 360(p + 5 - p)/p(p + 5) = 1

⇒ 360(5) = p² + 5p

⇒ 1800 = p² + 5p

⇒ p² + 5p - 1800 = 0

⇒ p² + 45p - 40p - 1800 = 0

⇒ p(p + 45) - 40(p + 45) = 0

⇒ (p + 45) (p - 40) = 0

⇒ p = -45

Also

⇒ p = 40

[As negative value is not APPLICABLE for speed]

So,

⇒ p = 40 km/hr.

Therefore,

Speed of the train = 40 km/h


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