A person rows a boat 10 kms along the stream in 30 minutes and returns to the starting point in 40 minutes.

The speed of the stream is:

The correct option is 2.5 km/h.

Let us solve this problem step-by-step to understand how to arrive at this answer.

Step 1: Understand the given values
The distance covered in one direction (along the stream, which is downstream) is 10 km.
The time taken to row downstream is 30 minutes.
The distance covered when returning (against the stream, which is upstream) is the same, 10 km.
The time taken to row upstream is 40 minutes.

Step 2: Convert time from minutes to hours
To find the speed in km/h, we first convert the time durations from minutes to hours:
Downstream time ($t_d$):
$t_d=\frac{30}{60}=0.5\text{ hours}$
Upstream time ($t_u$):
$t_u=\frac{40}{60}=\frac{2}{3}\text{ hours}$

Step 3: Calculate downstream and upstream speeds
Downstream speed ($d$) is defined as:
$d=\frac{\text{Distance}}{t_d}=\frac{10}{0.5}=20\text{ km/h}$
Upstream speed ($u$) is defined as:
$u=\frac{\text{Distance}}{t_u}=\frac{10}{\left(\frac{2}{3}\right)}=10\times \frac{3}{2}=15\text{ km/h}$

Step 4: Find the speed of the stream
The speed of the stream ($y$) is calculated using the formula:
$y=\frac{d-u}{2}$
Substituting the calculated speeds into the formula:
$y=\frac{20-15}{2}=\frac{5}{2}=2.5\text{ km/h}$
Thus, the speed of the stream is 2.5 km/h.