Question : $S_1$ and $S_2$ are two stations that are 195 km apart. A train starts from $S_1$ at 4:00 pm and moves towards $S_2$ at the speed of 65 km/hr. Another train starts from $S_2$ at 5:00 pm and moves towards $S_1$ at the speed of 35 km/hr. At what time will the two trains meet?
Option 1: 6:06 pm
Option 2: 6:30 pm
Option 3: 6:15 pm
Option 4: 6:18 pm
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Correct Answer: 6:18 pm
Solution : Given: The distance between stations $S_1$ and $S_2$ is 195 km. Speed of the train which starts at 4:00 pm from station $S_1$ = 65 km/hr Speed of the train which starts at 5:00 pm from station $S_2$ = 35 km/hr The train starts from $S_1$ at 4:00 pm and in 1 hour, it covers 65 km. Therefore th e remaining distance at 5:00 pm = 195 – 65 = 130 km The time taken by the trains, when they meet $=\frac{130}{65 + 35}= 1.3$ hours $=1.3×60=78$ minutes = 1 hour 18 minutes So, the required time = 5:00 pm + 1 hour 18 minutes = 6:18 pm Hence, the correct answer is 6:18 pm.
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