In an office, `40%` of the staff is female. `70%` of the female staff and `50%` of the male staff are married. The percentage of the unmarried staff in the office is

Options

A. `64%`/Percentage
B. `54%`/Percentage
C. `60%`/Percentage
D. `42%`/Percentage

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the total number of staff
Let the total number of staff in the office be 100 (for simplicity in calculations).

### Step 2: Calculate the number of female staff
Since 40% of the staff is female:
\[ \text{Number of females} = 40\% \text{ of } 100 = 40 \]

### Step 3: Calculate the number of male staff
The number of male staff can be calculated as:
\[ \text{Number of males} = 100 - \text{Number of females} = 100 - 40 = 60 \]

### Step 4: Calculate the number of married female staff
70% of the female staff is married:
\[ \text{Married females} = 70\% \text{ of } 40 = \frac{70}{100} \times 40 = 28 \]

### Step 5: Calculate the number of unmarried female staff
The number of unmarried female staff is:
\[ \text{Unmarried females} = \text{Total females} - \text{Married females} = 40 - 28 = 12 \]

### Step 6: Calculate the number of married male staff
50% of the male staff is married:
\[ \text{Married males} = 50\% \text{ of } 60 = \frac{50}{100} \times 60 = 30 \]

### Step 7: Calculate the number of unmarried male staff
The number of unmarried male staff is:
\[ \text{Unmarried males} = \text{Total males} - \text{Married males} = 60 - 30 = 30 \]

### Step 8: Calculate the total number of unmarried staff
The total number of unmarried staff is:
\[ \text{Unmarried staff} = \text{Unmarried females} + \text{Unmarried males} = 12 + 30 = 42 \]

### Step 9: Calculate the percentage of unmarried staff
The percentage of unmarried staff in the office is:
\[ \text{Percentage of unmarried staff} = \left(\frac{\text{Unmarried staff}}{\text{Total staff}}\right) \times 100 = \left(\frac{42}{100}\right) \times 100 = 42\% \]

### Final Answer
The percentage of unmarried staff in the office is **42%**.

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