A river 2 km wide is flowing at the rate of 2km/hr. A boatman, can row the boat at a speed of 4 km/hr in still water, goes a distance of 2 km upstream and them comes back. The time taken by him to complete his journey is

Options

A. Statement-I is true, Statement-II is true, Statement-II is correct explanation for Statement-I
B. Statement-I is true, Statement-II is true, Statement-II is NOT a correct explanation for Statement-I
C. Statement-I is true, Statement-II is false
D. Statement-I is false, Statement-II is true.

Explanation

To solve the problem, we need to calculate the time taken by the boatman to row upstream and downstream in the river. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Speeds
- The speed of the river (current) is \( u = 2 \) km/hr.
- The speed of the boat in still water is \( v = 4 \) km/hr.

### Step 2: Calculate Effective Speeds
**Upstream Speed:**
- When the boat is going upstream, the effective speed of the boat is given by:
\[ v_{\text{upstream}} = v - u = 4 \text{ km/hr} - 2 \text{ km/hr} = 2 \text{ km/hr} \]

**Downstream Speed:**
- When the boat is going downstream, the effective speed of the boat is given by:
\[ v_{\text{downstream}} = v + u = 4 \text{ km/hr} + 2 \text{ km/hr} = 6 \text{ km/hr} \]

### Step 3: Calculate Time for Each Journey
**Distance for Each Journey:**
- The distance the boatman rows upstream is \( 2 \) km and the same distance downstream is also \( 2 \) km.

**Time Taken Upstream:**
- The time taken to row upstream is calculated using the formula:
\[ t_{\text{upstream}} = \frac{\text{Distance}}{\text{Speed}} = \frac{2 \text{ km}}{2 \text{ km/hr}} = 1 \text{ hour} \]

**Time Taken Downstream:**
- The time taken to row downstream is calculated similarly:
\[ t_{\text{downstream}} = \frac{\text{Distance}}{\text{Speed}} = \frac{2 \text{ km}}{6 \text{ km/hr}} = \frac{1}{3} \text{ hour} \]

### Step 4: Calculate Total Time
- The total time taken for the entire journey (upstream and downstream) is:
\[ t_{\text{total}} = t_{\text{upstream}} + t_{\text{downstream}} = 1 \text{ hour} + \frac{1}{3} \text{ hour} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \text{ hours} \]

### Step 5: Convert Total Time to Minutes
- To convert the total time from hours to minutes:
\[ t_{\text{total}} = \frac{4}{3} \text{ hours} \times 60 \text{ minutes/hour} = 80 \text{ minutes} \]

### Final Answer
The total time taken by the boatman to complete his journey is **80 minutes**.

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