Rampur is 100 km from Sitapur. At 3 pm bharat Express leaves Rampur for Sitapur and travels at a constant speed of 30 km/h. One hour later, Laxman Mail leaves Sitapur for Rampur and travels at a constant speed of 40 kmph’. Each train makes one stop only at a station 10 km from its starting point and remains there for 15 min.Which train is nearer to Rampur when they meet?

Bharat express:

3:00- start from Rampur

3:20 reach stoppage

3:35 start for Sitapur

4:30 30*55/60 = 330/12 = 27.5 km travel since 3:35

Total travel till 4:30 = 27.5 + 30/3 = 37.5 km

Laxman Mail:

4:00 at Sitapur

4:15 reach stopage

4:30 start for Rampur

Total travel till 4:30 = 10 kms

Time after two trains meet = distance between them/Relative speed

t = 90-37.5/70 = 0.75 hrs = 45 min

5:15 meeting of 2 trains

At 5:15. 

Bharat express from Rampur = 37.5 + 45/60 * 30 = 60 kms

Laxman Mail from Rampur = 100 - {10+45/60 * 40} = 100 - 40 = 60 kms

So both trains are equidistant from Rampur.