How i solve this optional chapter question, of exercise 3.7 in easiest way . I think it is also an important type of question. 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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# 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. Q.3

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Let the speed of the train be A km/hr and the time taken by the train to travel a distance be N hours and the distance to travel be X hours.

Speed of the train = Distance travelled by train / Time taken to travel that distance

A = N (distance)/ X (time)

Or, N = AX â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ (1)

Using the information that is given, we get:

(A+10) = X/(N-2)

(A + 10) (N â€“ 2) = X

AN + 10N â€“ 2A â€“ 20 = X

By using the equation (1) we get,

â€“ 2A + 10N = 20 â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ (2)

(A-10) = X/(N+3)

(A â€“ 10) (N + 3) = X

AN â€“ 10N + 3A â€“ 30 = X

By using the equation (1) we get,

3A â€“ 10N = 30 â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ â€“ (3)

Adding equation (2) and equation (3) we get,

A = 50

Using the equation (2) we get,

(-2) x (50) + 10N = 20

-100 +10N = 20

=> 10N = 120

N = 12hours

From the equation (1) we get,

Distance travelled by the train, X = AN

= 50 x 12

= 600 km

Hence, the distance covered by the train is 600km.