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A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

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300 km

400 km

600 km

260 km

answer is C.

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Detailed Solution

Concept- In order to solve the given problem, first we will consider original time taken, speed of train and distance as T, S, and D respectively. Then use the formula,

Speed = \frac{Distance}{Time}

Here,

Let speed of train be x km / h

And time taken by h .

Total distance = xy km .

So in Case 1:
Speed increased by 10 km/h and time was reduced by 2 hours.
Distance traveled remains xy km.

(x + y) (y - 2) = xy

Then,

xy - 2 x + 10 y - 20 = xy

2 x + 10 y - 20 = 0

2 x + 10 y = 20 \dots \dots \dots \dots (1)

Now in case 2:
Speed decreased by 10km/h, and time taken increased by 3 hours.
Distance traveled remains xy km.

(x - 10) (y + 3) = xy

Then,

xy + 3 x - 10 y - 30 = xy

3 x - 10 y - 30 = 0

3 x - 10 y = 30 \dots \dots \dots . . (2)

Therefore,

x = 50 km / h

Putting this in Equations 2, we will get,

3 \times 50 - 10 y = 30

150 - 10 y = 30

y = 12

Then,

Distance is 50 \times 12 = 600 km .

Hence, the correct answer is 600 km.

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A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

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