Veena and Karmesh were at different places in Delhi. They fixed a meeting point to meet to settle some issue. Veena started her journey at 8:00 a.m. from place A and reached place B at 4:00 p.m. and Karmesh started moving from place B 2 hours later than the time Veena started and could reach place A at 5:00 p.m. the same day, via the same route. At what time will Karmesh and Veena meet each other?

Let's calculate the total time taken by each person:
Veena starts at 8:00 a.m. and reaches at 4:00 p.m.

Time taken by Veena (T
V
​
)=8 hours
Karmesh starts 2 hours later than Veena, so he starts at 8:00 a.m.+2 hours=10:00 a.m. He reaches at 5:00 p.m.

Time taken by Karmesh (T
K
​
)=7 hours
Let the total distance between A and B be the LCM of 8 and 7, which is 56 units.

Speed of Veena (S
V
​
)=
8
56
​
=7 units/hour

Speed of Karmesh (S
K
​
)=
7
56
​
=8 units/hour

Veena starts at 8:00 a.m., and Karmesh starts at 10:00 a.m. In these 2 hours (from 8:00 a.m. to 10:00 a.m.), Veena covers:

Distance covered by Veena=7×2=14 units
Remaining distance between them at 10:00 a.m.:

Remaining distance=56−14=42 units
At 10:00 a.m., both are moving towards each other, so their relative speed is:

Relative speed=S
V
​
+S
K
​
=7+8=15 units/hour
Time taken to meet after 10:00 a.m.:

Time=
15
42
​
=
5
14
​
=2
5
4
​
 hours
2 hours+(
5
4
​
×60) minutes=2 hours 48 minutes
Meeting time =10:00 a.m.+2 hours 48 minutes=12:48 p.m.