Question : A person goes from P to Q in 8 hours. He starts from P at 8 a.m. Another person goes from Q to P in 12 hours. He starts from Q at 9 a.m. At what time will they meet?
Option 1: 1:12 p.m.
Option 2: 12:12 p.m.
Option 3: 12:20 p.m.
Option 4: 1:20 p.m.
Correct Answer: 1:12 p.m.
Solution :
The LCM of 8 and 12 is 24 which can be assumed as the total distance between P and Q.
Speed of first-person = $\frac{24}{8}$ = 3 km/h
Speed of first-person = $\frac{24}{12}$ = 2 km/h
The first person started one hour earlier than the second person. So the distance covered by the first person in that first hour is 3 km.
Remaining distance = 24 - 3 = 21
Time taken by both of them to meet each other = $\frac{21}{(3+2)} = \frac{21}{5}$ = 4.2 hr
So the time when they will meet each other = 9 + 4.2
= 9 hr + 4 hr + 12 minutes
= 1∶12 p.m.
Hence, the correct answer is 1:12 p.m.
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