Meeting time of two buses
XAT 2026 · Quantitative Ability & Data Interpretation · Medium · Time Speed Distance
Two buses travel between Jamshedpur and Kolkata in the opposite directions, on the same road. On that road, the maximum allowed speeds are different (but constant) for the opposite directions. Usually, both buses travel at the respective maximum allowed speeds to their respective destinations: the bus from Jamshedpur to Kolkata takes , while the bus from Kolkata to Jamshedpur takes .
One day, the two buses start at the same time. However, one hour after starting, the bus from Jamshedpur to Kolkata reduces its speed to half of its maximum allowed speed due to congestion on the road.
If both buses do not stop anywhere in between, how many hours after starting do they meet?
- A.
2 hours
- B.
23/12 hours
- C.
12/5 hours
- D.
21/11 hours
- E.
10/11 hours
D
Explanation
Let the distance between Jamshedpur and Kolkata be . Speed of Bus 1 (Jamshedpur to Kolkata) = . Speed of Bus 2 (Kolkata to Jamshedpur) = .
In : Bus 1 travels . Bus 2 travels . Remaining distance = .
After , Bus 1 reduces speed to . Relative speed = . Time taken to cover remaining distance = .
Total time elapsed from starting = .
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