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

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50 km/h

40 km/h

35 km/h

30 km/h

answer is B.

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Detailed Solution

Given that a train travels 360 km at a uniform speed.
Also, if the speed had been 5 km/h more, it would have taken 1 hour less for the same journey.
Let the speed of train be n km/h.
We know,

T i m e = D i s t a n c e S p e e d

Let the time taken by train to cover distance of 360 km =

360 n

hour.
Speed of the train increased by 5 km = n + 5.
Let the new time taken by train to cover distance of 360 km =

360 n + 5

hour.
As the train time decreased by 1 hour, if the speed is increased, the difference of the time taken before and after increase of speed is 1.
Now,

360 n − 360 n + 5 = 1

Form the quadratic equation.
Take L.C.M n and (n+5), we get

⇒ 360 n − 360 n + 5 = 1 ⇒ 360 (n + 5) − 360 n n (n + 5) = 1 ⇒ 360 n + 1800 − 360 n n 2 + 5 n = 1 ⇒ 1800 = n 2 + 5 n ⇒ n 2 + 5 n − 1800 = 0

⇒ n 2 + 45 n − 40 n − 1800 = 0 ⇒ n (n + 45) − 40 (n + 45) = 0 ⇒ (n + 45) (n − 40) = 0 ⇒ n + 45 or n − 40 = 0 ⇒ n = − 45 or n = 40

We got our two speeds of train as n=-45 and n=40.
But the speed of the train can never be negative.
So, the speed of the train is n=40 km/h.
Therefore, the correct option is 2.

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