Rahul covers 734 km in a boat in 30 hours against the stream and he takes 12 hours with the stream then find the speed of the stream?

Correct option is A

Given: 

Distance = 734 km

Time taken against the stream = 30 hours

Time taken with the stream = 12 hours 

Speed of the stream = ? 

Solution: 

​Let the speed of the boat in still water be $b$ km/h, and the speed of the stream be $s$ km/h.

Against the stream:   When Rahul moves against the current, his effective speed becomes b−s.

With the stream:   When Rahul moves with the current, his effective speed becomes b+s.

Against the stream: Rahul covers 734 km in 30 hours, so:

​$$\frac{734}{b - s} = 30$$ 

​Simplifying this:

$$\quad b - s = \frac{734}{30} = 24.47 \, \text{km/h}$$  

With the stream: Rahul covers 734 km in 12 hours, so: 

​$$\frac{734}{b + s} = 12$$​​

This simplifies to: 

​$$\quad b + s = \frac{734}{12} = 61.17 \, \text{km/h}$$ 

We now have the system of two equations:

b − s = 24.47

b + s = 61.17 

Adding these two equations:

​$$(b−s)+(b+s)=24.47+61.17$$ 

$$2b=85.64$$ 

$$\quad b = \frac{85.64}{2} = 42.82 \, \text{km/h}$$ 

Now, substitute $b=42.82$ into the second equation:​

b + s = 61.17

42.82 + s = 61.17 

$$s=61.17−42.82=18.35km/h$$ 

Thus the speed of the stream is approximately 18.35 km/h