A boat goes 27 km upstream and 33 km downstream in 6 hours. In the same time it can go 36 km upstream and 22 km downstream. How much time will it take to go 36 km upstream and 44 km downstream?

8 h

We know that,

Speed of boat = a kmph and Speed of stream = b kmph

Speed of upstream = (a - b) kmph

Speed of downstream = (a + b) kmph

We have,

Time taken in going 27km upstream and 33km downstream = 6 hours

Time taken in going 36km upstream and 22km downstream = 6 hours

According to the question,

= 33/(a + b) + 27/(a - b) = 6

= 22/(a + b) + 36/(a - b) = 6

Then,

= 33/(a + b) + 27/(a - b) = 22/(a + b) + 36/(a - b)

= 11/(a + b) = 9/(a - b) 

= 11a - 11b = 9a + 9b

= 2a = 20b

= a = 10b

Then,

= 33/(10b + b) + 27/(10b - b) = 6

= 3/b + 3/b = 6

= b = 1

= a = 10

Speed downstream = 10 + 1 = 11 kmph

Speed upstream = 10 - 1 = 9 kmph

Then,

= Time taken to go 44 km downstream = 44/11 + 36/9 = 8 hours