A motorboat whose speed is 20 km/h in still water takes 30 minutes more to go 24 km upstream than to cover the same distance downstream. If the speed of the boat in still water is increased by 2 km/h, then how much time will it take to go 39 km downstream and 30 km upstream?

3 h 10 m

For the short solution try value putting method, 

According to the question, 

30 min = 1/2 hr

x = 20 (Speed in still water)

= 24/(20 - y) - 24/(20 + y) = 1/2

Here the R.H.S is 1/2, so the value of 20 - y must be more than 12

Hence take y = 4 (so that right bracket will become 1 as 20 + 4 = 24) and (left bracket will be more than half)

= 24/(20 - 4) - 24(20 + 4) = 3/2 - 1 = 1/2

Hence the value of Y = 4

Now according to the question, 

= 39/(22 + 4) + 30/(22 - 4) = 39/26 + 30/18

= 19/6 = 3(1/6) = 3 hours and 10 min