The ratio of the speed of a boat downstream to its speed upstream is 5:3. The boat takes a total of 16 hours to cover P km downstream and P km upstream. Find the time taken by the boat to cover 4P km in still water.

ATQ, Let the upstream speed of the boat be 3x kmph. The ratio of downstream speed to upstream speed = 5:3. So, downstream speed = 5x kmph. Upstream speed = 3x kmph. Speed of boat in still water = (Downstream speed + Upstream speed) ÷ 2. Speed of boat in still water = (5x + 3x) ÷ 2 = 8x ÷ 2 = 4x kmph. Now, the boat covers P km downstream and P km upstream in a total of 16 hours. Time taken downstream = P ÷ 5x. Time taken upstream = P ÷ 3x. Let P ÷ x = y. Then P ÷ 5x = y ÷ 5. And P ÷ 3x = y ÷ 3. Total time = y ÷ 5 + y ÷ 3. Given total time = 16 hours. So, y ÷ 5 + y ÷ 3 = 16. This means 8y ÷ 15 = 16. 8y = 16 × 15 = 240. y = 240 ÷ 8 = 30. So, P ÷ x = 30. Now, we need to find the time taken to cover 4P km in still water. Still water speed = 4x. Required time = 4P ÷ 4x. Required time = P ÷ x. Since P ÷ x = 30, required time = 30 hours.