Question

A boy runs for 10 min. at a uniform speed of 9 km/hr. At what speed should he run for the next 20 min. so that the average speed comes 12 km/hr?

Answer 1

Average speed (12km/hr) = Total Distance / Total Time
                         D1 + D2 / T1 + T2
Total Time = 10 min + 20 min = 30 min = 1/2 Hour
D1 = Speed * Time = 9 * 1/6 (10 min = 1/6 hr)
= 3/2 km = 1.5 km
D2 = ?
12 = 1.5 + D2 / 1/2
12 * 1/2 = 1.5 + D2
6 = 1.5 + D2
6 - 1.5 = D2
4.5 km = D2
Speed = Distance / Time
           = 4.5 / 1/3 (20 min = 1/3 hr)
           = 4.5 * 3 (Reciprocal)
           = 13.5 km/hr

Answer 2

Let us solve this in a different way.

Boy runs for first 10 min at 9 kmph  = 9 km/hr
Let boy run for next 10 min at V kmph
let boy run for next 10 min at V kmph

His average speed is  average of above three. 
Average speed =  (9+ 2 V) / 3   =  12 kmph
So    9 + 2 V = 3 * 12 = 36
2 V = 36 - 9 = 27

V = 27/2 = 13.5 km/hr