Two persons A and B get the same salary. Their basic pay are different. The allowances are 65% and 80% of the basic pay respectively. What is the ratio of the basic pay ?

Options

A. `17:15`
B. `7:5`
C. `11:10`
D. `12:11`

Explanation

To solve the problem step by step, we will determine the ratio of the basic pay of persons A and B based on the information given about their allowances.

### Step-by-Step Solution:

1. **Define Basic Pays**:
Let the basic pay of person A be \( x \) and the basic pay of person B be \( y \).

2. **Calculate Allowances**:
- The allowance for A is 65% of \( x \), which can be expressed as:
\[ \text{Allowance of A} = 0.65x \]
- The allowance for B is 80% of \( y \), which can be expressed as:
\[ \text{Allowance of B} = 0.80y \]

3. **Set Up the Salary Equation**:
Since both A and B receive the same total salary, we can write the equation:
\[ x + 0.65x = y + 0.80y \]

4. **Simplify the Equation**:
- For A:
\[ x + 0.65x = 1.65x \]
- For B:
\[ y + 0.80y = 1.80y \]
Therefore, we have:
\[ 1.65x = 1.80y \]

5. **Rearranging for the Ratio**:
To find the ratio of \( x \) to \( y \), we can rearrange the equation:
\[ \frac{x}{y} = \frac{1.80}{1.65} \]

6. **Simplifying the Ratio**:
- To simplify \( \frac{1.80}{1.65} \), we can multiply both the numerator and the denominator by 100 to eliminate the decimals:
\[ \frac{180}{165} \]
- Now, we can simplify this fraction by dividing both the numerator and the denominator by 15:
\[ \frac{180 \div 15}{165 \div 15} = \frac{12}{11} \]

7. **Final Ratio**:
Thus, the ratio of the basic pay of A to B is:
\[ x : y = 12 : 11 \]

### Conclusion:
The ratio of the basic pay of A to B is \( 12 : 11 \).