Keshav can row 60 km downstream and 36 km upstream ,taking 10 h each time .What is the velocity of the current?

Options

A. 3 km/h
B. 2.2 km/h
C. 4 km/h
D. 1.2 km/h

Answer

To solve the problem, we need to find the velocity of the current (R) using the information given about Keshav's rowing downstream and upstream.

### Step-by-Step Solution

1. **Understand the Problem**:
Keshav rows 60 km downstream and 36 km upstream, taking 10 hours for each trip. We need to find the velocity of the current (R).

2. **Define Variables**:
- Let K be Keshav's rowing speed in still water (in km/h).
- Let R be the velocity of the current (in km/h).

3. **Set Up Equations**:
- When rowing downstream, Keshav's effective speed is (K + R). The distance is 60 km, and the time taken is 10 hours.
\[ \text{Downstream speed equation: } \frac{60}{10} = K + R \implies K + R = 6 \quad \text{(1)} \]

- When rowing upstream, Keshav's effective speed is (K - R). The distance is 36 km, and the time taken is also 10 hours.
\[ \text{Upstream speed equation: } \frac{36}{10} = K - R \implies K - R = 3.6 \quad \text{(2)} \]

4. **Solve the Equations**:
- From equation (1):
\[ K + R = 6 \]
- From equation (2):
\[ K - R = 3.6 \]

- Now, we can add these two equations:
\[ (K + R) + (K - R) = 6 + 3.6 \]
\[ 2K = 9.6 \implies K = \frac{9.6}{2} = 4.8 \quad \text{(Keshav's speed in still water)} \]

- Now, substitute K back into equation (1) to find R:
\[ 4.8 + R = 6 \implies R = 6 - 4.8 = 1.2 \quad \text{(velocity of the current)} \]

5. **Final Answer**:
The velocity of the current (R) is **1.2 km/h**.