A train left point A at 12 noon. Two hours later, another train started from point A in the same direction. It overtook the first train at 8 PM. It is known that the sum of the speeds of the two trains is 140 km/hr. Then, at what time would the second train overtake the first train, if instead the second train had started from point A in the same direction 5 hours after the first train? Assume that both the trains travel at constant speeds.
Explanation:
Case 1: Train 2 starts 2 hours after Train 1. Train 1 travels from 12 pm till 8 pm i.e., for 8 hours. Same distance is travelled by Train 2 from 2 pm till 8 pm i.e., in 6 hours. ∴ Ratio of speeds of Train 1 and Train 2 = 6 : 8 = 3 : 4 ⇒ Let speed of Train 1 = 3x and Train 2 = 4x ⇒ 3x + 4x = 140 ⇒ x = 20
⇒ Speed of Train 1 = 60 kmph, Speed of Train 2 = 80 kmph.
Case 2: Train 2 starts 5 hours after Train 1. Train 1 would have travelled 5 × 60 = 300 kms when Train 2 starts i.e., at 5 pm. Relative speed of the two trains = 80 - 60 = 20 kmph. ∴ Time for Train 2 after it starts to meet Train 1 = 300/20 = 15 hours.
⇒ 15 hours after 5 pm = 8 am the next day.
Hence, option (c).
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