Suppose a man swims 12 km upstream and 20 km downstream in a river in 4 hours. If he swims 18 km upstream and 10 km downstream also in 4 hours, then the speed at which he swims in the still water is.

Correct option is C

Given:
Time is taken to move 12 km upstream and 20 km downstream = 4 hours
Time is taken to move 18 km upstream and 10 km downstream = 4 hours
Formula Used:
Speed of the boat in upstream = Speed of boat in still water - Speed of stream = x - y 
Speed of boat in downstream = Speed of boat in still water + Speed of stream = x + y 
Solution:
Let speed of boat in still water and speed of stream be x and y respectively.
Then according to the question,
​$$\frac{12}{x - y} + \frac{20}{x + y} = 4 \quad \text{--- (1)}$$ 

$$\frac{18}{x - y} + \frac{10}{x + y} = 4 \quad \text{--- (2)}$$ 
Multiply by 2 in equation (2)
​$$\frac{36}{x - y} + \frac{20}{x + y} = 8$$ ....(3)
Subtract equation 3 and 1, we get
​$$\frac{-24}{x - y} = -4$$​​
x- y = 6 ..............(4)
Put the value of x-y in equation (1)
​$$\frac{12}{6} + \frac{20}{x + y} = 4\\\frac{20}{x + y} = 2\\ x + y = 10 ...........(5)$$
On adding equation 4 and 5, we get

x = 8km/hr and y = 2km/hr 
At 8 km/hr speed he can swims in still water.