A steamer goes downstream from one port to another in 4 hours. It covers the same distance upstream in 5 hours. If the speed of stream is 2 km/ hr, the distance between the two ports is

Options

A. 50 km
B. 60 km
C. 70 km
D. 80 km

Answer

To solve the problem, we need to determine the distance between two ports based on the time taken by a steamer to travel downstream and upstream, along with the speed of the stream.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the speed of the steamer in still water be \( x \) km/hr.
- The speed of the stream is given as \( 2 \) km/hr.

2. **Calculate Downstream Speed:**
- When the steamer is going downstream, its effective speed is the sum of its speed in still water and the speed of the stream:
\[ \text{Downstream speed} = x + 2 \text{ km/hr} \]

3. **Calculate Upstream Speed:**
- When the steamer is going upstream, its effective speed is the difference between its speed in still water and the speed of the stream:
\[ \text{Upstream speed} = x - 2 \text{ km/hr} \]

4. **Use Time and Distance Relationship:**
- The distance covered downstream in 4 hours can be expressed as:
\[ \text{Distance} = \text{Speed} \times \text{Time} = (x + 2) \times 4 \]
- The distance covered upstream in 5 hours can be expressed as:
\[ \text{Distance} = \text{Speed} \times \text{Time} = (x - 2) \times 5 \]

5. **Set Up the Equation:**
- Since the distance covered downstream and upstream is the same, we can set the two expressions equal to each other:
\[ 4(x + 2) = 5(x - 2) \]

6. **Expand and Simplify the Equation:**
- Expanding both sides:
\[ 4x + 8 = 5x - 10 \]
- Rearranging the equation:
\[ 8 + 10 = 5x - 4x \]
\[ 18 = x \]

7. **Calculate the Distance:**
- Now that we have the value of \( x \), we can substitute it back to find the distance:
\[ \text{Distance} = 4(x + 2) = 4(18 + 2) = 4 \times 20 = 80 \text{ km} \]

### Final Answer:
The distance between the two ports is **80 km**.