Q41 of 186 Page 4

A train travels a distance of 300 km at a constant speed. If the speed of SE the 2O train is increased by 5 km an hour, the journey would have taken 2 hours less. Find the original speed of the train.

Total distance travelled = 300km

Let the speed of train = x km/hr


We know that,



Hence, time taken by train


According to the question,


Speed of the train is increased by 5km an hour


∴ the new speed of the train = (x + 5)km/hr


Time taken to cover 300km


Given that time taken is 2hrs less from the previous time




⇒ 300x + 1500 – 300x = 2x (x + 5)


⇒ 1500 = 2x2 + 10x


⇒ 750 = x2 + 5x


⇒ x2 + 5x – 750 = 0


⇒ x2 + 30x – 25x – 750 = 0


⇒ x (x + 30) – 25 (x + 30) = 0


⇒ (x – 25) (x + 30) = 0


⇒ (x – 25) = 0 or (x + 30) = 0


∴ x = 25 or x = – 30


Since, speed can’t be negative.


Hence, the speed of the train is 25km/hr


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