A passenger train departs from Delhi at 6 pm for Mumbai

A passenger train departs from Delhi at 6 pm for Mumbai. At 9 pm, an express train, whose average speed exceeds that of the passenger train by 15 km/hour leaves Mumbai for Delhi. Two trains meet each other mid-route. At what time do they meet, given that the distance between the cities is 1080 km?

  1. 4 p.m.
  2. 2 a.m
  3. 12 midnight
  4. 6 a.m.

Answer

The distance between the cities is 1080 km. As the trains meet each other mid-route, each train travels distance of 540 km.

Let the speed of train traveling from Delhi to Mumbai be s. Let the time taken by this train be t.

st = 540

s = 540/t

Speed of train traveling from Mumbai to Delhi = s+15

Time taken by train traveling from Mumbai to Delhi = t-3

st = (s+15)(t-3)

st = st - 3s + 15t - 45

- 3(540/t) + 15t - 45 = 0

t2 - 3t - 108 = 0

t2 - 12t + 9t - 108 = 0

t(t - 12) + 9(t - 12) = 0

(t - 12)(t + 9) = 0

t = 12 (as time cannot be negative)

6 pm + 12 hours = 6 am

The correct option is D.