24- carat gold is pure gold
18- carat gold is 3/4 gold.
20-carat gold is 5/6 gold.
The ratio to pure gold in 18 carat gold to 20 carat gold is

Options

A. `5:8`
B. `10:9`
C. `15:24`
D. `9:10`

Explanation

To find the ratio of pure gold in 18-carat gold to pure gold in 20-carat gold, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the definitions**:
- 24-carat gold is considered pure gold (100% gold).
- 18-carat gold is \( \frac{3}{4} \) gold.
- 20-carat gold is \( \frac{5}{6} \) gold.

2. **Set a common quantity for comparison**:
- Let's assume we have a total quantity of gold, say \( X \) grams. This will help us compare the amounts of pure gold in both types of gold.

3. **Calculate the amount of pure gold in 18-carat gold**:
- The amount of pure gold in 18-carat gold is \( \frac{3}{4} \) of \( X \):
\[ \text{Pure gold in 18-carat gold} = \frac{3}{4}X \]

4. **Calculate the amount of pure gold in 20-carat gold**:
- The amount of pure gold in 20-carat gold is \( \frac{5}{6} \) of \( X \):
\[ \text{Pure gold in 20-carat gold} = \frac{5}{6}X \]

5. **Set up the ratio**:
- The ratio of pure gold in 18-carat gold to pure gold in 20-carat gold is:
\[ \text{Ratio} = \frac{\frac{3}{4}X}{\frac{5}{6}X} \]

6. **Simplify the ratio**:
- The \( X \) cancels out:
\[ \text{Ratio} = \frac{3}{4} \div \frac{5}{6} = \frac{3}{4} \times \frac{6}{5} \]
- Now, multiply the fractions:
\[ = \frac{3 \times 6}{4 \times 5} = \frac{18}{20} \]

7. **Reduce the fraction**:
- Simplifying \( \frac{18}{20} \) gives:
\[ = \frac{9}{10} \]

8. **Final answer**:
- The ratio of pure gold in 18-carat gold to pure gold in 20-carat gold is \( \frac{9}{10} \).