In an office, 70% of the total number of employees are females. 80% of the total number of employees, including 85 females, got promotion. If there are 105 female employees, then what percentage of male employees got protion ?

Options

A. `87%`
B. `77(7)/(9)%`
C. `35%`
D. `67%`

Answer

To solve the problem step by step, we will follow the given information and perform calculations accordingly.

### Step 1: Determine the Total Number of Employees
We know that 70% of the total number of employees are females and that there are 105 female employees.

Let the total number of employees be \( x \).

From the information given:
\[ 0.7x = 105 \]

To find \( x \):
\[ x = \frac{105}{0.7} = 150 \]

### Step 2: Calculate the Number of Male Employees
Since we have the total number of employees, we can find the number of male employees.

Total employees = 150
Number of female employees = 105
Number of male employees = Total employees - Female employees
\[ \text{Male employees} = 150 - 105 = 45 \]

### Step 3: Determine the Number of Employees Who Got Promotion
We know that 80% of the total employees got promoted.

Calculating the number of employees who got promoted:
\[ \text{Promoted employees} = 0.8 \times 150 = 120 \]

### Step 4: Calculate the Number of Female Employees Who Got Promotion
It is given that 85 females got promoted.

### Step 5: Calculate the Number of Male Employees Who Got Promotion
To find the number of male employees who got promoted, we subtract the number of females who got promoted from the total number of promoted employees:
\[ \text{Male employees promoted} = \text{Total promoted} - \text{Females promoted} \]
\[ \text{Male employees promoted} = 120 - 85 = 35 \]

### Step 6: Calculate the Percentage of Male Employees Who Got Promotion
Now, we can find the percentage of male employees who got promoted:
\[ \text{Percentage of males promoted} = \left( \frac{\text{Male employees promoted}}{\text{Total male employees}} \right) \times 100 \]
\[ \text{Percentage of males promoted} = \left( \frac{35}{45} \right) \times 100 \]
\[ \text{Percentage of males promoted} = \frac{35 \times 100}{45} = \frac{3500}{45} \approx 77.78\% \]

### Final Answer
Thus, the percentage of male employees who got promoted is approximately \( 77.78\% \), which can be expressed as \( 77 \frac{7}{9}\% \).