Arjun takes 5 hrs to swim a upstream of 40km where as he takes only 2 hrs to swim downstream of 24km. Find the speed in still water.
A)15 kmph
B)10 kmph
C)12kmph
D)9kmph

Options

A. 15 kmph
B. 10 kmph
C. 12kmph
D. 9kmph

Answer

To find the speed of Arjun in still water, we can break down the problem step by step.

### Step 1: Define Variables
Let:
- \( x \) = speed of the boat 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. Arjun swims upstream 40 km in 5 hours.
2. Arjun swims downstream 24 km in 2 hours.

Using the formula for speed, which is \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \), we can set up the following equations:

**For upstream:**
- Speed upstream = \( x - y \)
- Time taken = 5 hours
- Distance = 40 km

So, we have:
\[ x - y = \frac{40}{5} = 8 \quad \text{(Equation 1)} \]

**For downstream:**
- Speed downstream = \( x + y \)
- Time taken = 2 hours
- Distance = 24 km

So, we have:
\[ x + y = \frac{24}{2} = 12 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
Now we have two equations:
1. \( x - y = 8 \)
2. \( x + y = 12 \)

We can solve these equations simultaneously.

**Add Equation 1 and Equation 2:**
\[ (x - y) + (x + y) = 8 + 12 \]
This simplifies to:
\[ 2x = 20 \implies x = 10 \]

**Substitute \( x \) back into one of the equations to find \( y \):**
Using Equation 1:
\[ 10 - y = 8 \implies y = 2 \]

### Step 4: Conclusion
The speed of the boat in still water \( x \) is 10 km/h.

### Final Answer
The speed in still water is **10 km/h** (Option B).

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