The ratio of the total amount distributed in all the males and females as salary is 6: 5. The ratio of the salary of each male and female is 2: 3. Find the ratio of the no. of males and females.

Options

A. 5:9
B. 5:7
C. 7:5
D. 9:5

Answer

To solve the problem, we need to find the ratio of the number of males to the number of females based on the given salary ratios.

### Step-by-Step Solution:

1. **Define Variables**:
Let the number of males be \( A \) and the number of females be \( B \).

2. **Understand Salary Ratios**:
We know that the total salary distributed among males and females is in the ratio of \( 6:5 \). This means:
\[ \text{Total Salary of Males} : \text{Total Salary of Females} = 6 : 5 \]

3. **Salary per Male and Female**:
The salary ratio of each male to each female is given as \( 2:3 \). Let the salary of each male be \( 2x \) and the salary of each female be \( 3x \) for some \( x \).

4. **Express Total Salaries**:
The total salary for all males can be expressed as:
\[ \text{Total Salary of Males} = A \cdot (2x) = 2Ax \]
The total salary for all females can be expressed as:
\[ \text{Total Salary of Females} = B \cdot (3x) = 3Bx \]

5. **Set Up the Ratio**:
According to the given ratio of total salaries:
\[ \frac{2Ax}{3Bx} = \frac{6}{5} \]
The \( x \) cancels out, simplifying to:
\[ \frac{2A}{3B} = \frac{6}{5} \]

6. **Cross Multiply**:
Cross multiplying gives:
\[ 2A \cdot 5 = 6 \cdot 3B \]
Simplifying this, we have:
\[ 10A = 18B \]

7. **Find the Ratio of A to B**:
Dividing both sides by 2:
\[ 5A = 9B \]
Rearranging gives:
\[ \frac{A}{B} = \frac{9}{5} \]

8. **Conclusion**:
Therefore, the ratio of the number of males to the number of females is:
\[ \text{Ratio of Males to Females} = 9:5 \]