A fisherman can row 2km against the stream in 20 minutes and return in 15 minutes. The speed of current is ? Options are (a) 1 km/hr (b) 2 km/hr (c) 3 km/hr (d) None of the above.

Options

A. 1 km/hr
B. 2 km/hr
C. 3 km/hr
D. None of the above

Answer

To solve the problem step by step, we need to determine the speed of the current based on the information given about the fisherman rowing against and with the stream.

### Step 1: Understand the problem
The fisherman rows 2 km against the stream in 20 minutes and returns in 15 minutes. We need to find the speed of the current.

### Step 2: Convert time from minutes to hours
- Time taken to row upstream (against the current): 20 minutes = 20/60 hours = 1/3 hours
- Time taken to row downstream (with the current): 15 minutes = 15/60 hours = 1/4 hours

### Step 3: Define variables
Let:
- \( x \) = speed of the fisherman in km/hr
- \( y \) = speed of the current in km/hr

### Step 4: Set up equations based on distance = speed × time
1. **For upstream (against the current)**:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ 2 = (x - y) \times \frac{1}{3} \]
Multiplying both sides by 3 gives:
\[ 6 = x - y \quad \text{(Equation 1)} \]

2. **For downstream (with the current)**:
\[ 2 = (x + y) \times \frac{1}{4} \]
Multiplying both sides by 4 gives:
\[ 8 = x + y \quad \text{(Equation 2)} \]

### Step 5: Solve the equations
Now we have two equations:
1. \( x - y = 6 \)
2. \( x + y = 8 \)

We can solve these equations using the elimination method.

### Step 6: Add the two equations
Adding Equation 1 and Equation 2:
\[ (x - y) + (x + y) = 6 + 8 \]
This simplifies to:
\[ 2x = 14 \]
Dividing by 2 gives:
\[ x = 7 \]

### Step 7: Substitute to find \( y \)
Now substitute \( x = 7 \) back into Equation 2:
\[ 7 + y = 8 \]
Subtracting 7 from both sides gives:
\[ y = 1 \]

### Step 8: Conclusion
The speed of the current \( y \) is 1 km/hr.

### Final Answer
The speed of the current is **1 km/hr**. The correct option is (a) 1 km/hr.