A person can row with the stream at 8 km/h and against the stream at 4 km/h. The speed of the current is (In km/hr)

Options

A. 1
B. 2
C. 1.5
D. 4

Answer

To solve the problem, we need to determine the speed of the current (stream). Let's denote:

- Speed of the person in still water = x km/h
- Speed of the current = y km/h

From the problem, we know:

1. The speed of the person rowing with the stream (downstream) is given as 8 km/h.
2. The speed of the person rowing against the stream (upstream) is given as 4 km/h.

Using the relationship between these speeds, we can set up the following equations:

1. When rowing with the stream:
\[ x + y = 8 \quad \text{(1)} \]

2. When rowing against the stream:
\[ x - y = 4 \quad \text{(2)} \]

Now, we can solve these two equations step by step.

### Step 1: Add both equations
We add equations (1) and (2):
\[ (x + y) + (x - y) = 8 + 4 \]
This simplifies to:
\[ 2x = 12 \]

### Step 2: Solve for x
Now, divide both sides by 2:
\[ x = \frac{12}{2} = 6 \quad \text{(3)} \]

### Step 3: Substitute x back into one of the equations
Now that we have the value of x, we can substitute it back into either equation (1) or (2) to find y. We will use equation (1):
\[ 6 + y = 8 \]

### Step 4: Solve for y
Subtract 6 from both sides:
\[ y = 8 - 6 = 2 \quad \text{(4)} \]

### Conclusion
The speed of the current (y) is 2 km/h.

### Final Answer
The speed of the current is **2 km/h**.

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