Question

A train runs from jaipur at 10:00 am and travels to delhi at 3:00 p.M. The second train runs from 11:00 pm to delhi and arrives at 6:00 pm to find the time to meet?

Answer 1

Suppose the trains reach T hours after 10 am at their destination.

⇒ Train towards Delhi took T hours and train towards Jaipur took (T – 1) hours to reach their destination.

Let speed of train towards Delhi be S km/hr. Since, both trains travelled equal distances, speed will be inversely proportional to time.

⇒ Speed of train moving towards Jaipur = (ST)/(T – 1)

At 1 pm, the sum of distances that had been travelled by them together is 90% of distance between Delhi and Jaipur.

By 1 pm, train towards Delhi has travelled for 3 hours and train towards Jaipur has travelled for 2 hours.

Also, distance between Jaipur and Delhi = ST

⇒ Sum of distances = 3 × S + 2 × (ST)/(T – 1) = (90/100) × ST

⇒ 3 + 2 × (T/(T – 1)) = 0.9T

⇒ 3T – 3 + 2T = 0.9T2 – 0.9T

⇒ 0.9T2 – 5.9T + 3 = 0

⇒ 9T2 – 59T + 30 = 0

⇒ (9T – 5)(T – 6) = 0

This gives T = 5/9 hours or T = 6 hours.

Since, 5/9 < 1, this case is not possible as first train would reach destination before 11 am, and hence cannot meet second train in between.

⇒ T = 6 hours

∴ Trains will reach their destinations at 6 hours after 10 am; i.e., at 4 pm.