A diver rowing at the speed of 3 km/h in still water takes double the time going 50 km upstream compared to going 50 km downstream. The speed of the diver against the stream is:

Correct option is D

Given:

Speed of diver in still water = 3 km/h.

Distance to travel=  50 km

The time taken upstream is double the time taken downstream.

speed of the diver against the stream = ?

Solution: 

Let Speed of stream is  $x$ km/h.

Speed of diver upstream = 3− x km/h (since the stream slows the diver down).

Speed of diver downstream = 3 + x km/h (since the stream helps the diver).

We are told that the diver takes twice the time to go upstream compared to downstream 

Time taken to travel 50 km upstream:

​$$\text{Time upstream} = \frac{50}{3 - x}$$ 

Time taken to travel 50 km downstream:

​$$\text{Time downstream} = \frac{50}{3 + x}$$ 

​According to the problem, the time taken upstream is twice the time taken downstream:

​$$\frac{50}{3 - x} = 2 \times \frac{50}{3 + x}$$ 

$$\frac{1}{3 - x} = 2 \times \frac{1}{3 + x}$$ 

cross-multiply to eliminate the fractions:

$$(3 + x) = 2(3 - x)$$ 

3 + x = 6 − 2x 

x + 2x = 6 - 3

3x = 3 

x = $$\frac{3}{3}$$ = 1

Thus Speed of stream is 1 km/h

Substitute the value of x:

Speed of diver upstream = 3− x km/h = 3 - 1 = 2 km/h

Thus the speed of the diver against the stream is 2 km/h.