Question : Anil and Tirath drove between two points, A and B, 192 km apart. Anil started the journey from point A at 8:20 am, drove at a speed of 64 km/hr, reached point B, and immediately returned to A at the same speed. Tirath started the journey from point A at 9:50 am, drove at a speed of 96 km/hr, reached point B, and immediately returned to A at the same speed. At what time did Anil and Tirath first meet each other?
Option 1: 11:38 am
Option 2: 11:28 am
Option 3: 11:43 am
Option 4: 11:33 am
Correct Answer: 11:38 am
Solution :
Given: The distance between Point A and B is 192 km.
Anil's speed is 64 km/hr.
So, it will take $\frac{192}{64} = 3$ hours for Anil to reach point B.
He started at 8:20 am. So, he will reach point B at 8:20 + 3 = 11:20 am
Tirath's speed is 96 km/hr.
Since Tirath starts his journey at 9:50 am,
At 11:20, when Anil reaches point B, Tirath will be (96 × 1.5) = 144 km from A.
Now, at 11:20, the distance between Anil and Tirath is (192 – 144) = 48 km
Their relative speed is (64 + 96) = 160 km/hr
So, they will meet after $\frac{60 × 48}{160} =18$ minutes
Therefore, Tirath and Anil will meet each other at (11:20 + 18) = 11:38 am
Hence, the correct answer is 11:38 am.
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