A man can swim 3 km/hr in still water. If the velocity of the stream be 2 km/hr, the time taken by him to swim to a place 10km upstream and back is:

Options

A. `8(1)/(3)` hr.
B. `9(1)/(2)`hr.
C. 10 hr
D. 12 hr

Answer

To solve the problem step by step, we need to determine the time taken by a man to swim 10 km upstream and then return back downstream.

### Step 1: Identify the speeds
- The speed of the man in still water = 3 km/hr
- The speed of the stream = 2 km/hr

### Step 2: Calculate the effective speed upstream
When swimming upstream, the effective speed is reduced by the speed of the stream:
\[ \text{Speed upstream} = \text{Speed of man} - \text{Speed of stream} = 3 \text{ km/hr} - 2 \text{ km/hr} = 1 \text{ km/hr} \]

### Step 3: Calculate the effective speed downstream
When swimming downstream, the effective speed is increased by the speed of the stream:
\[ \text{Speed downstream} = \text{Speed of man} + \text{Speed of stream} = 3 \text{ km/hr} + 2 \text{ km/hr} = 5 \text{ km/hr} \]

### Step 4: Calculate the time taken to swim upstream
The distance to swim upstream is 10 km. Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
The time taken to swim upstream is:
\[ \text{Time upstream} = \frac{10 \text{ km}}{1 \text{ km/hr}} = 10 \text{ hours} \]

### Step 5: Calculate the time taken to swim downstream
The distance to swim downstream is also 10 km. Using the same formula:
\[ \text{Time downstream} = \frac{10 \text{ km}}{5 \text{ km/hr}} = 2 \text{ hours} \]

### Step 6: Calculate the total time taken for the round trip
Now, we add the time taken to swim upstream and downstream:
\[ \text{Total time} = \text{Time upstream} + \text{Time downstream} = 10 \text{ hours} + 2 \text{ hours} = 12 \text{ hours} \]

Thus, the total time taken by the man to swim to a place 10 km upstream and back is **12 hours**.