Question : A train starts from a station $P$ for another station $Q$ at 6 p.m. at an average speed of 75 km/h. Another train starts from station $Q$ for station $\mathrm{P}$ at 8 p.m. at an average speed of 105 km/h. If the distance between these two stations is 690 km, then at what time will the two trains meet?
Option 1: 10:30 p.m.
Option 2: 10 p.m.
Option 3: 11 p.m.
Option 4: 11:30 p.m.
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Correct Answer: 11 p.m.
Solution :
The first train travels for 2 hours before the second train starts.
The distance covered in 2 hours = 2 × 75 = 150 km.
The remaining distance between the two trains when the second train starts = 690 – 150 = 540 km.
Both trains are moving towards each other.
The relative speed = 75 + 105 = 180 km/h
We know, $\text{Time}=\frac{\text{Distance}}{{\text{Speed}}}$
The time taken by two trains = $\frac{540}{180}$ = 3 hrs
The two trains will meet 3 hours after the second train starts.
i.e. 8 p.m. + 3 hr = 11 p.m.
Hence, the correct answer is 11 p.m.
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