The ratio of Pankaj's and Prakash's initial speeds was 3:2, let the total distance between A and B be 5

*x*. Therefore, Pankaj covered a distance of 3

*x* and Prakash covered 2

*x* before they met. Since they travelled for 2 hours, their initial speeds were 1.5

*x* and

*x* respectively.

After breakfast, their speeds reduced to half, so they were 0.75

*x* and 0.5

*x* respectively. Both of them travelled for 1 hr in opposite directions.

∴ The distance between them at 10 a.m. = 0.75

*x* + 0.5

*x* = 1.25

*x*Now, Prakash starts running at 2.5 times his present speed, which means at 1.25

*x*.

Pankaj is walking at 0.75

*x* in the same direction and is 1.25

*x* ahead of him.

∴ He would meet Pankaj at 12:30 p.m.

Hence, option 2.