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?
Answer & explanation
Correct answer: option 3
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