Solution

Given:• A car overtakes a goods train in 8 seconds

• The length of the goods train = 400 m

• The speed of the goods train = 36 kph = (\(36 * \frac{5}{18}\)) m/s = 10 m/s

• The same car crosses another goods train from opposite direction in 4 seconds

• Speed of the 2nd goods train = 54 kph = (\(54 * \frac{5}{18}\)) m/s = 15 m/s

o Hence, 2nd train is faster than 1st train, as its speed is more than 1st train

To find:• The time the faster train will take to overtake the slower train

Approach and Working: As the length of the car is negligible compared to the length of either of the trains, only the lengths of the trains need to be considered while considering the cases

Let us assume the speed of the car as u m/s and length of the 2nd train as l m

• In the 1st case, the car overtakes the 1st goods train in 8 seconds

o Total distance travelled = 400 m [only the length of the train]

o Relative speed = (u – 10) m/s

o Therefore, 8 (u – 10) = 400

Or, u – 10 = 50

Or, u = 60 m/s

• Hence, the speed of the car = 60 m/s

• In the 2nd case, the car crosses the 2nd train from opposite direction in 4 seconds

o Total distance travelled = l m [only the length of the train]

o Relative speed = (60 + 15) m/s = 75 m/s

o Therefore, 75 * 4 = l

Or, l = 300 m

• Hence, the length of the 2nd train = 300 m

• When the 2nd train overtakes the 1st train,

o Total distance travelled = (400 + 300) m = 700 m

o Relative speed = (15 – 10) m/s = 5 m/s

o Therefore, the time taken to overtake = 700/5 secs = 140 secs = 2 minutes 20 seconds

Hence, the correct answer is option C.

Answer: CFirst of all thank you for the complete solution but i have a small doubt in last few lines:

o Therefore, the time taken to overtake = 700/5 secs = 140 secs = 2 minutes 20 seconds[/list]

Here relative speed should be added as both trains are moving in opposite direction. and in that case answer will be 28sec.

So kindly guide me where I am going wrong in understanding the ques.