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?

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 second person = $$\frac{24}{12}$$ = 2 km/h

First person started one hour earlier than the second person. So the distance covered by first person in that first hour is 3 km.

Remaining distance = 24-3 = 21 km

Time taken by both of them to meet each other = $$\frac{21}{3+2}$$

= $$\frac{21}{5}$$

= 4.2 hours

So the time when they will meet each other = 9 a.m. + 4.2 hours

= 9 a.m. + 4 hours 12 minutes [we know that 1 hour = 60 minutes. So 0.2 hours = 12 minutes.]

= 1:12 pm