A man’s speed in still water is 4 km/h more than the speed of the current. If the man takes a total of 10 h to cover 45 km downstream and 35 km upstream, then the speed of the man in still water is:

The correct option is 20 km/h.

Let us break down the problem step-by-step:

Step 1: Define the variables
Let the speed of the man in still water be $x$ km/h.
Let the speed of the stream current be $y$ km/h.
According to the question, the man's speed in still water is 4 km/h more than the speed of the current:
$x=y+4$
This can also be written as:
$y=x-4$

Step 2: Find the downstream and upstream speeds
The speed of the man while traveling downstream (in the direction of the current) is the sum of his speed in still water and the speed of the current:
$\text{Downstream Speed}=x+y=x+(x-4)=2x-4$ km/h.

The speed of the man while traveling upstream (against the direction of the current) is the difference between his speed in still water and the speed of the current:
$\text{Upstream Speed}=x-y=x-(x-4)=4$ km/h.

Step 3: Set up the time equation
We know that:
$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

The man takes a total of 10 hours to cover 45 km downstream and 35 km upstream. Therefore, we can write the equation as:
$\frac{45}{2x-4}+\frac{35}{4}=10$

Step 4: Solve for $x$
Subtract $\frac{35}{4}$ from both sides of the equation:
$\frac{45}{2x-4}=10-\frac{35}{4}$

Simplify the right side:
$\frac{45}{2x-4}=\frac{40-35}{4}$

$\frac{45}{2x-4}=\frac{5}{4}$

Cross-multiply to solve for $x$:
$5(2x-4)=45\times 4$

Divide both sides by 5:
$2x-4=9\times 4$

$2x-4=36$

Add 4 to both sides:
$2x=40$

Divide by 2:
$x=20$

Thus, the speed of the man in still water is 20 km/h.