A boat takes 12 hours to go downstream and 24 hours to return while covering a certain
distance. What is the time taken by the boat to cover the same distance in still water?

Correct option is C

Given:

- Time taken downstream: 12 hours.
- Time taken upstream: 24 hours.
- Let the distance covered be D
- Let the speed of the boat in still water be B and the speed of the current be C .

Formula Used:

- Speed downstream = B + C .
- Speed upstream = B - C .
-$$Time = \frac{\text{Distance}}{\text{Speed}} .$$​​

Solution:

From the given data:

Downstream speed: B + C = $$\frac{D}{12}$$​​

Upstream speed: B - C = $$\frac{D}{24}$$​​

Adding equations (1) and (2):

The speed of the boat in still water is  $$\frac{D}{16} .$$​​

To find the time taken in still water:

​$$Time = \frac{\text{Distance}}{\text{Speed}}\\\ \\\text{Time} = \frac{D}{B} \\\ \\\\text{Time} = \frac{D}{D/16}\\\ \\\text{Time} = 16 \text{ hours}$$​​

The boat takes 16 hours to cover the same distance in still water.