A train starts from a Jaipur towards Delhi at 10 am. Another train starts from Delhi towards Jaipur at 11 am. Both reach their destinations at same time. At 1 pm, the sum of distances that had been travelled by them together is 90% of distance between Delhi and Jaipur. At what time did they reach their destinations?
Solution
Correct Answer: Option D
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.
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