The average monthly salary of all the employees in an industry is Rs 12,000. The average salary of male employees Is Rs 15,000 and that of female employees is Rs 8,000. What is the ratio of male employees to female employees ?

Options

A. `5:2`
B. `3:4`
C. `4:3`
D. `2:5`

Answer

To find the ratio of male employees to female employees based on their average salaries, we can use the concept of averages and the formula for the average salary of a group.

### Step-by-Step Solution:

1. **Define Variables:**
Let the number of male employees be \( M \) and the number of female employees be \( F \).

2. **Write the Average Salary Equation:**
The average salary of all employees can be expressed as:
\[ \text{Average Salary} = \frac{\text{Total Salary of Males} + \text{Total Salary of Females}}{M + F} \]
Given that the average salary of all employees is Rs 12,000, we can write:
\[ 12000 = \frac{15000M + 8000F}{M + F} \]

3. **Cross Multiply to Eliminate the Fraction:**
Multiply both sides by \( (M + F) \):
\[ 12000(M + F) = 15000M + 8000F \]

4. **Expand and Rearrange the Equation:**
Expanding the left side gives:
\[ 12000M + 12000F = 15000M + 8000F \]
Rearranging the equation leads to:
\[ 12000M + 12000F - 15000M - 8000F = 0 \]
Simplifying this gives:
\[ -3000M + 4000F = 0 \]

5. **Solve for the Ratio:**
Rearranging the equation gives:
\[ 3000M = 4000F \]
Dividing both sides by 1000:
\[ 3M = 4F \]
Thus, the ratio of male employees to female employees is:
\[ \frac{M}{F} = \frac{4}{3} \]

### Final Answer:
The ratio of male employees to female employees is \( 4:3 \).