There are three departments (H.R., Sales & Finance) in company Z. The ratio of males to females in H.R. is $7:10$. The number of females in Finance is $20\%$ more than the number of females in H.R. The number of males in Finance is 6 more than the number of females in Finance. The average number of males in all departments is 39, and the number of males in Sales is 35. The number of females in Sales is $25\%$ more than the number of females in Finance.

What percent more or less is the number of females in the Sales department compared to the number of females in the H.R. department?

Question

There are three departments (H.R., Sales & Finance) in company Z. The ratio of males to females in H.R. is $7:10$. The number of females in Finance is $20\%$ more than the number of females in H.R. The number of males in Finance is 6 more than the number of females in Finance. The average number of males in all departments is 39, and the number of males in Sales is 35. The number of females in Sales is $25\%$ more than the number of females in Finance.

What percent more or less is the number of females in the Sales department compared to the number of females in the H.R. department?

Accepted Answer

**Solution:**

1. Let the number of females in H.R. be $10x$ and males be $7x$ (given ratio $7:10$).

2. Number of females in Finance = $20\%$ more than females in H.R.:
   $$	ext{Females in Finance} = 10x + 0.20 	imes 10x = 12x$$

3. Number of males in Finance = females in Finance + 6:
   $$	ext{Males in Finance} = 12x + 6$$

4. Average number of males in all departments is 39, so total males in all departments:
   $$3 	imes 39 = 117$$

5. Males in Sales = 35 (given).

6. Total males = males in H.R. + males in Finance + males in Sales:
   $$7x + (12x + 6) + 35 = 117$$
   $$7x + 12x + 6 + 35 = 117$$
   $$19x + 41 = 117$$
   $$19x = 117 - 41 = 76$$
   $$x = \frac{76}{19} = 4$$

7. Females in H.R. = $10x = 10 	imes 4 = 40$

8. Females in Finance = $12x = 12 	imes 4 = 48$

9. Females in Sales = $25\%$ more than females in Finance:
   $$48 + 0.25 	imes 48 = 48 + 12 = 60$$

10. Now, find the percentage increase of females in Sales compared to females in H.R.:
    $$\frac{60 - 40}{40} 	imes 100 = \frac{20}{40} 	imes 100 = 50\%$$

**Answer:** 50\%

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