The difference between time taken by boat-A to cover 80 km upstream and that taken to cover 80 km downstream is 1 hour. If the respective ratio between its upstream and downstream speeds is 4:5, what distance will boat-A cover downstream in 2 hours? (in km)

Options

A. 48
B. 32
C. 40
D. 44

Answer

To solve the problem, we need to find the distance that boat-A will cover downstream in 2 hours, given the information about its upstream and downstream speeds.

### Step-by-Step Solution:

1. **Define the Speeds**:
Let the upstream speed of boat-A be \(4x\) km/h and the downstream speed be \(5x\) km/h, based on the given ratio of 4:5.

2. **Calculate Time Taken**:
The time taken to cover 80 km upstream is given by the formula:
\[ \text{Time}_{\text{upstream}} = \frac{\text{Distance}}{\text{Speed}} = \frac{80}{4x} = \frac{20}{x} \text{ hours} \]
The time taken to cover 80 km downstream is:
\[ \text{Time}_{\text{downstream}} = \frac{80}{5x} = \frac{16}{x} \text{ hours} \]

3. **Set Up the Equation**:
According to the problem, the difference in time taken between upstream and downstream is 1 hour:
\[ \text{Time}_{\text{upstream}} - \text{Time}_{\text{downstream}} = 1 \]
Substituting the expressions we found:
\[ \frac{20}{x} - \frac{16}{x} = 1 \]

4. **Solve for \(x\)**:
Simplifying the left-hand side:
\[ \frac{20 - 16}{x} = 1 \implies \frac{4}{x} = 1 \]
Cross-multiplying gives:
\[ 4 = x \]

5. **Find the Downstream Speed**:
Now that we have \(x\), we can find the downstream speed:
\[ \text{Downstream Speed} = 5x = 5 \times 4 = 20 \text{ km/h} \]

6. **Calculate the Distance Covered in 2 Hours**:
The distance covered downstream in 2 hours can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 20 \text{ km/h} \times 2 \text{ hours} = 40 \text{ km} \]

### Final Answer:
The distance that boat-A will cover downstream in 2 hours is **40 km**.