70 males and 100 females are working in a firm. During one mass recruitment drive, an equal number of males and females are recruited and their ratio becomes 3 : 4. The total number of people working in the firm after recruitment is:

Options

A. 240
B. 200
C. 210
D. 220

Answer

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

1. **Identify the initial number of males and females:**
- Males = 70
- Females = 100

2. **Let the number of males and females recruited be \( x \):**
- After recruitment, the number of males will be \( 70 + x \).
- After recruitment, the number of females will be \( 100 + x \).

3. **Set up the ratio equation:**
- The problem states that the ratio of males to females becomes \( 3:4 \) after recruitment.
- Therefore, we can write the equation:
\[ \frac{70 + x}{100 + x} = \frac{3}{4} \]

4. **Cross-multiply to eliminate the fraction:**
- Cross-multiplying gives:
\[ 4(70 + x) = 3(100 + x) \]

5. **Expand both sides:**
- Expanding gives:
\[ 280 + 4x = 300 + 3x \]

6. **Rearranging the equation:**
- Subtract \( 3x \) from both sides:
\[ 280 + 4x - 3x = 300 \]
- This simplifies to:
\[ 280 + x = 300 \]

7. **Solve for \( x \):**
- Subtract 280 from both sides:
\[ x = 300 - 280 \]
- Therefore:
\[ x = 20 \]

8. **Calculate the total number of people after recruitment:**
- The total number of people after recruitment will be:
\[ \text{Total} = (70 + x) + (100 + x) = (70 + 20) + (100 + 20) = 90 + 120 = 210 \]

9. **Final answer:**
- The total number of people working in the firm after recruitment is **210**.