Question : Two cities P and Q are 181 km apart on a straight road. One man starts from P at 8:30 a.m. and travels toward Q at 30 km/hr. If another man starts from Q at 8:54 a.m. and travels towards P at a speed of 35 km/hr, then at what time will they meet?
Option 1: 11:30 a.m.
Option 2: 10:00 a.m.
Option 3: 10.30 a.m.
Option 4: 11:00 a.m.
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Correct Answer: 11:30 a.m.
Solution : Distance between P and Q at 8:30 a.m. = 181 km Distance covered by P until Q starts = $30 \times \frac{24}{60}$ = 12 km Distance between P and Q at 8:54 a.m. = 181 − 12 = 169 km Let the time taken to cover 169 km be $t$ hours. So, now both persons have to travel 169 km combined $⇒30t + 35t = 169$ $⇒65t = 169$ $⇒t = \frac{169}{65}= 2 \frac{39}{65} =$ 2 hours 36 minutes Therefore, the time of the meeting = 8:54 a.m. + 2 hours 36 minutes = 11:30 a.m. Hence, the correct answer is 11:30 a.m.
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