The ratio between weights of gold and silver in an alloy is `17:3.` If the weight of silver in the alloy is `2.7 g,` find :
the weight of gold in the alloy.

Answer

To find the weight of gold in the alloy given the ratio of gold to silver and the weight of silver, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Ratio**:
The ratio of the weight of gold to the weight of silver in the alloy is given as \( 17:3 \).

2. **Identify the Weight of Silver**:
The weight of silver in the alloy is given as \( 2.7 \, \text{g} \).

3. **Set Up the Equation**:
Let the weight of gold be represented as \( x \, \text{g} \). According to the ratio, we can express this relationship as:
\[ \frac{x}{2.7} = \frac{17}{3} \]

4. **Cross-Multiply to Solve for \( x \)**:
To eliminate the fraction, we can cross-multiply:
\[ 3x = 17 \times 2.7 \]

5. **Calculate \( 17 \times 2.7 \)**:
First, calculate \( 17 \times 2.7 \):
\[ 17 \times 2.7 = 45.9 \]
So, we have:
\[ 3x = 45.9 \]

6. **Divide by 3 to Find \( x \)**:
Now, divide both sides by 3 to isolate \( x \):
\[ x = \frac{45.9}{3} \]

7. **Calculate \( \frac{45.9}{3} \)**:
Performing the division gives:
\[ x = 15.3 \]

8. **Conclusion**:
Therefore, the weight of gold in the alloy is:
\[ \text{Weight of gold} = 15.3 \, \text{g} \]

### Final Answer:
The weight of gold in the alloy is \( 15.3 \, \text{g} \).

---