Aditya can row with stream at 10 km/h and against the stream at 6 km/h. His speed in still water is

Options

A. 16 km/h
B. 6 km/h
C. 8 km/h
D. 10 km/h

Answer

To find Aditya's speed in still water, we can use the information given about his rowing speeds with and against the stream. Let's break down the solution step by step.

### Step 1: Define Variables
Let:
- \( x \) = Aditya's speed in still water (in km/h)
- \( y \) = speed of the stream (in km/h)

### Step 2: Set Up Equations
From the problem, we know:
1. When rowing with the stream (downstream), the speed is \( x + y = 10 \) km/h.
2. When rowing against the stream (upstream), the speed is \( x - y = 6 \) km/h.

### Step 3: Write the System of Equations
We can write the two equations based on the information:
1. \( x + y = 10 \) (1)
2. \( x - y = 6 \) (2)

### Step 4: Solve the System of Equations
To solve for \( x \) and \( y \), we can add equations (1) and (2):

\[ (x + y) + (x - y) = 10 + 6 \]
This simplifies to:
\[ 2x = 16 \]

Now, divide both sides by 2:
\[ x = 8 \text{ km/h} \]

### Step 5: Find the Speed of the Stream
Now, we can substitute \( x \) back into one of the original equations to find \( y \). Using equation (1):
\[ 8 + y = 10 \]
Subtract 8 from both sides:
\[ y = 2 \text{ km/h} \]

### Conclusion
Aditya's speed in still water is \( 8 \) km/h.

### Final Answer
The speed in still water is **8 km/h**.