A man can row his boat at speed of 4km/hr and he finds that the time taken rowing upstream is double to that taken downstream. Find the speed of the stream (in km/hr)
A. 1.5
B. 1.3
C. 2
D. 1

Options

A. D
B. A
C. B
D. C

Answer

To solve the problem, we can follow these steps:

### Step 1: Define Variables
Let the speed of the stream be \( x \) km/hr. The speed of the man rowing the boat is given as 4 km/hr.

### Step 2: Determine Upstream and Downstream Speeds
- **Upstream Speed**: When rowing upstream, the effective speed of the boat is reduced by the speed of the stream. Thus, the upstream speed is:
\[ \text{Upstream Speed} = 4 - x \text{ km/hr} \]

- **Downstream Speed**: When rowing downstream, the effective speed of the boat is increased by the speed of the stream. Thus, the downstream speed is:
\[ \text{Downstream Speed} = 4 + x \text{ km/hr} \]

### Step 3: Set Up the Time Relationship
According to the problem, the time taken to row upstream is double the time taken to row downstream. If we let \( d \) be the distance traveled, then:

- **Time taken upstream**:
\[ \text{Time}_{\text{upstream}} = \frac{d}{4 - x} \]

- **Time taken downstream**:
\[ \text{Time}_{\text{downstream}} = \frac{d}{4 + x} \]

Given that the upstream time is double the downstream time, we can write:
\[ \frac{d}{4 - x} = 2 \cdot \frac{d}{4 + x} \]

### Step 4: Simplify the Equation
Since \( d \) is common on both sides, we can cancel it out (assuming \( d \neq 0 \)):
\[ \frac{1}{4 - x} = \frac{2}{4 + x} \]

### Step 5: Cross Multiply
Cross multiplying gives:
\[ 4 + x = 2(4 - x) \]

### Step 6: Expand and Rearrange
Expanding the right side:
\[ 4 + x = 8 - 2x \]

Now, rearranging the equation:
\[ x + 2x = 8 - 4 \]
\[ 3x = 4 \]

### Step 7: Solve for \( x \)
Dividing both sides by 3:
\[ x = \frac{4}{3} \approx 1.33 \text{ km/hr} \]

### Step 8: Conclusion
Thus, the speed of the stream is approximately \( 1.33 \) km/hr, which rounds to \( 1.3 \) km/hr.

### Final Answer
The speed of the stream is \( \text{B. } 1.3 \text{ km/hr} \).

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