The distance between two cities A and B is 330 km. A train starts from A at 8 am and travels towards B at 60 km/hr. Another train starts from B at 9 am and travels towards A at 75 km/hr. At what time do they meet ?

Solution(By Examveda Team)

Time = $$\frac{270}{60 + 75}$$
Time = 2 hours
So, time at which they meet = 11.00 am

Alternate
Assume that they meet x hours after 8 am
Then,
Train 1, starting from A, travels x hours till the trains meet
Distance travelled by train 1 in x hours = 60x km

Train 2, starting from B, travels (x - 1) hours till the trains meet
Distance travelled by train 2 in (x - 1)hours = 75(x - 1) km

Total distance travelled
= Distance travelled by train 1 + Distance travelled by train 2
⇒ 330 = 60x + 75(x -1)
⇒ 12x + 15(x - 1) = 66
⇒ 12x + 15x - 15 = 66
⇒ 27x = 66 + 15 = 81
⇒ 3x = 9
⇒ x = 3
Hence, the trains meet 3 hours after 8 am, i.e. at 11 am