A boat can go 5 km upstreams and 7 km downstream in 45 minutes. It can also go 5 km downstream and 2.5 km upstream in 25 minutes. How much time (in minutes) will it take to go 6 km downstream?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 12.
Let the speed of the boat be 'a' and the speed of the stream be 'b' km/hr
According to the question,
⇒ 5/(a - b) + 7.5/(a + b) = 45/60 = 3/4...................(1)
⇒ 5/(a + b) + 2.5/(a - b) = 5/12...............(2)
By multiplying eq(2) by 2 and subtracting eq(1) from (2) we get,
⇒ 2.5/(a + b) = 1/12
⇒ a + b = 30
Time taken to cover 6 km downstream = 6/(a + b) × 60 = 6/30 × 60 = 12 minutes