A train covers a distance of 360 km at a uniform speed. Had the speed been 5km/hour more, it would have taken 48 minutes less for the journey. Find the original speed of the train.

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The original speed of the train is 35 km/hr.

The original speed of the train is 45 km/hr.

The original speed of the train is 55 km/hr.

The original speed of the train is 65 km/hr.

answer is B.

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Detailed Solution

Given that, distance travelled by train = 360 km
Let us assume usual speed of the train is x km/h.
Now, convert 48 minutes into hours.

48 minutes = 4860 hours since, 1 minute = 160 hours

We know that,
Time = Distance/speed
So, time taken to cover a distance of 360 km =

360 x hours

.
If the speed is increased by 5 km/h then the new speed of the train = (x + 5) km/h.
Time taken to cover a distance of 360 km at new speed =

360 (x + 5) hours

.
But it is given that the time, if the speed is increased, is 48 minutes or 4/5 hour less.
So,
Time taken by train in the first case - Time is taken by train in 2nd case = 4/5 hour Question Image

By cross multiplying the terms, we get,

x 2 + 5 x × 1 = 5 × 450 x 2 + 5 x − 2250 = 0

Let us compare the above equation with ax² + bx + c = 0, we get a = 1, b = 5 and
c = - 2250
We know that, the roots of the quadratic equation in the form ax² + bx + c = 0 are