Number of male and female employees work in four different companies i.e., P, Q, R, and S. Number of male employees in company P is 560, which is 100\% more than that of females. The ratio of male to female employees in company Q is 4:5, and the number of females in company P is equal to the number of male employees in company Q. The total number of males in all four companies is 1760, and the total number of employees in all four companies is 3500. The number of males in company S is 420, and the number of females in company R is 650.

Find the average number of female employees in all four companies.

Question

Number of male and female employees work in four different companies i.e., P, Q, R, and S. Number of male employees in company P is 560, which is 100\% more than that of females. The ratio of male to female employees in company Q is 4:5, and the number of females in company P is equal to the number of male employees in company Q. The total number of males in all four companies is 1760, and the total number of employees in all four companies is 3500. The number of males in company S is 420, and the number of females in company R is 650.

Find the average number of female employees in all four companies.

Accepted Answer

**Solution:**

1. Let the number of female employees in company P be *x*.

2. Given that the number of male employees in company P is 560, which is 100\% more than females:
   - This means males in P = females in P + 100\% of females in P = 2 * x
   - So, 2 * x =$ 560 \implies x = 280$

3. Number of females in company P = 280.

4. Number of male employees in company Q equals the number of females in company P, so males in Q = 280.

5. The ratio of male to female employees in company Q is 4:5.
   - Let males in Q = 4k and females in Q = 5k.
   - Since males in Q = 280, 4k =$ 280 \implies k = 70.$
   - Therefore, females in Q = 5 * 70 = 350.

6. Number of males in company S is given as 420.

7. Number of females in company R is 650.

8. Total males in all companies = 1760.
   - Males in P + Q + R + S = 1760
   - 560 + 280 + males in R + 420 = 1760
   - Males in R = 1760 - (560 + 280 + 420) = 1760 - 1260 = 500

9. Total employees in all companies = 3500.
   - Total employees = males + females = 3500
   - Total females = 3500 - total males = 3500 - 1760 = 1740

10. Females in P + Q + R + S = 1740
    - Females in P = 280
    - Females in Q = 350
    - Females in R = 650
    - Let females in S = y
    - So, 280 + 350 + 650 + y = 1740
    - y = 1740 - 1280 = 460

11. Average number of female employees in all four companies:
    $$\frac{280 + 350 + 650 + 460}{4} = \frac{1740}{4} = 435$$

**Answer:** 435

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