The speed of boat in still water is 500% more than speed of curent what is ratio speed of the boat downstream to the speed of boat upstream

Options

A. 12:7
B. 9:5
C. 7:5
D. 5:7

Answer

To solve the problem, we need to find the ratio of the speed of the boat downstream to the speed of the boat upstream, given that the speed of the boat in still water is 500% more than the speed of the current.

### Step-by-Step Solution:

1. **Define Variables**:
Let the speed of the current be \( y \) km/h.
The speed of the boat in still water is \( x \) km/h.

2. **Express the Speed of the Boat**:
According to the problem, the speed of the boat in still water is 500% more than the speed of the current.
This can be expressed mathematically as:
\[ x = y + 500\% \text{ of } y \]
Since 500% of \( y \) is \( 5y \), we can rewrite the equation as:
\[ x = y + 5y = 6y \]

3. **Calculate Downstream and Upstream Speeds**:
- The speed of the boat downstream (when moving with the current) is:
\[ \text{Downstream speed} = x + y = 6y + y = 7y \]
- The speed of the boat upstream (when moving against the current) is:
\[ \text{Upstream speed} = x - y = 6y - y = 5y \]

4. **Find the Ratio of Downstream to Upstream Speeds**:
Now we can find the ratio of the downstream speed to the upstream speed:
\[ \text{Ratio} = \frac{\text{Downstream speed}}{\text{Upstream speed}} = \frac{7y}{5y} \]
Simplifying this gives:
\[ \text{Ratio} = \frac{7}{5} \]

5. **Final Answer**:
Therefore, the ratio of the speed of the boat downstream to the speed of the boat upstream is:
\[ 7:5 \]