The distance between two stations, Delhi and Amritsar is 450 km. A train starts at 4 p.m. from Delhi and moves towards Amritsar at an average speed of 60 km/h. Another train starts from Amritsar at 3 : 20 p.m. and moves towards Delhi at an average speed of 80 km/h. At what distance from Delhi will the two trains meet?

Correct option is A

Given:

Distance between Delhi and Amritsar = 450km

Train A starts from Delhi at 4:00p.m. at 60km/hr

Train B starts from Amritsar at 3:20p.m. at 80km/hr

Formula Used:

Time = $$\frac{Distance}{Speed}$$​​

Distance = Speed $$\times$$​ Time

Solution:

Train B leaves early at 3:20pm hence distance travelled by train B in till 4:00pm will be:

Time = 40min =$$\frac{40}{60} = \frac{2}{3}hr$$​​

Distance = $$80 \times \frac{2}{3} = \frac{160}{3}km$$​​

Distance left =$$450 - \frac{160}{3} = \frac{1350- 160}{3} = \frac{1190}{3}km$$​​

Now at 4:00pm train A starts moving towars train B hence

Relative speed of both trains = 60 + 80 = 140 km/hr

Now time taken to cover the distance =$$\frac{\frac{1190}{3}}{140}= \frac{17}{6}= 2\frac{5}{6}hr$$​

Distance covered by train A in $$2\frac{5}{6}hr = 60 \times \frac{17}{6} =170km$$​​