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3. 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.

3. 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.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8740 Points
4 months ago
Solution: 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 – – – – – – – – – – – (1) Using the information that is given, we get: (A+10) = X/(N-2) (A + 10) (N – 2) = X AN + 10N – 2A – 20 = X By using the equation (1) we get, – 2A + 10N = 20 – – – – – – – – – – (2) (A-10) = X/(N+3) (A – 10) (N + 3) = X AN – 10N + 3A – 30 = X By using the equation (1) we get, 3A – 10N = 30 – – – – – – – – – (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.

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