Twice the speed downstream is equal to the thrice the speed upstream, the ratio of speed in still water to the speed of the current is:

Options

A. `1:5`
B. `5:1`
C. `1:3`
D. `2:320`

Answer

To solve the problem, we need to establish the relationship between the speeds of the boat in still water, the speed of the current, and the speeds downstream and upstream.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the speed of the boat in still water be \( B \).
- Let the speed of the current be \( S \).
- The speed downstream (with the current) can be expressed as \( B + S \).
- The speed upstream (against the current) can be expressed as \( B - S \).

2. **Set Up the Equation:**
- According to the problem, twice the speed downstream is equal to thrice the speed upstream:
\[ 2(B + S) = 3(B - S) \]

3. **Expand the Equation:**
- Expanding both sides gives:
\[ 2B + 2S = 3B - 3S \]

4. **Rearrange the Equation:**
- To isolate terms involving \( B \) and \( S \), we can rearrange the equation:
\[ 2B + 2S + 3S = 3B \]
\[ 2B + 5S = 3B \]

5. **Isolate \( B \):**
- Subtract \( 2B \) from both sides:
\[ 5S = 3B - 2B \]
\[ 5S = B \]

6. **Find the Ratio:**
- Now, we need to find the ratio of the speed in still water \( B \) to the speed of the current \( S \):
\[ \text{Ratio} = \frac{B}{S} = \frac{5S}{S} = 5 \]
- Therefore, the ratio of the speed in still water to the speed of the current is \( 5:1 \).

### Final Answer:
The ratio of the speed in still water to the speed of the current is \( 5:1 \).