Two numbers are 30% and 60% respectively more than a third number. The two numbers are in the ratio of :

Options

A. `13: 16`
B. `22 : 23`
C. `14 : 13`
D. `16 : 13`

Answer

To solve the problem, we need to find the ratio of two numbers that are 30% and 60% more than a third number. Let's denote the third number as \( z \).

### Step-by-Step Solution:

1. **Define the Third Number**:
Let the third number be \( z \).

2. **Calculate the First Number**:
The first number is 30% more than the third number.
\[ x = z + 0.3z = 1.3z \]

3. **Calculate the Second Number**:
The second number is 60% more than the third number.
\[ y = z + 0.6z = 1.6z \]

4. **Find the Ratio of the Two Numbers**:
We need to find the ratio \( \frac{x}{y} \).
\[ \frac{x}{y} = \frac{1.3z}{1.6z} \]
Here, \( z \) cancels out:
\[ \frac{x}{y} = \frac{1.3}{1.6} \]

5. **Simplify the Ratio**:
To simplify \( \frac{1.3}{1.6} \), we can multiply both the numerator and the denominator by 10 to eliminate the decimal:
\[ \frac{1.3 \times 10}{1.6 \times 10} = \frac{13}{16} \]

6. **Final Answer**:
Therefore, the ratio of the two numbers is:
\[ \frac{x}{y} = \frac{13}{16} \]