A boat goes a certain distance upstream and comes back downstream to the starting point in 72 min. If the speed of the boat in still water becomes 66.67% of the original, the time taken for the same journey will be 112 min. What is the ratio of the speed of the boat in still water and the speed of the current?

A boat goes a certain distance upstream and comes back downstream to the starting point in 72 min. If the speed of the boat in still water becomes 66.67% of the original, the time taken for the same journey will be 112 min. What is the ratio of the speed of the boat in still water and the speed of the current? Correct Answer 6 : 1

Calculations:

Let the distance be D and Speed of boat in still water be 3B and that of current be C

⇒ D/(3B + C) + D/(3B - C) = 72      ----(i)

When the speed of the boat becomes 66.67% → new boat speed = 2B

⇒ D/(2B + C) + D/(2B - C) = 112      ----(ii)

∴ Dividing eq. (i) by eq. (ii)

⇒ 6B/(3B + C)(3B - C)/4B/(2B + C)(2B - C) = 72/112

⇒ 6 × (4B² – C²)/4 × (9B² – C²) = 9/14

⇒ (4B² – C²)/(9B² – C²) = 3/7

⇒ B² = 4C² → B/C = 2/1

⇒ 3B/C = 6/1

The ratio of speed of boat and current in 6 : 1.