The average weight of all the 200 employees in an office is 68.2 kg, where $$\frac{2}{5}$$ of the employees are women and the ratio of the average weight of a man to that of a woman is 7 : 5. Find the average weight of the woman employees.

The average weight of all the 200 employees in an office is 68.2 kg, where $$\frac{2}{5}$$ of the employees are women.

Total employees = 200

Number of women employees = $$200\times\frac{2}{5}\ $$ = 80

Number of men employees = 200-80 = 120

the ratio of the average weight of a man to that of a woman is 7 : 5.

Let's assume the average weight of a man to that of a woman is 7y and 5y.

$$average\ weight\ all\ employees\ =\ \frac{men\ employees\times average\ weight\ of\ men\ employees+women\ employees\times average\ weight\ of\ women\ employees}{total\ employees}$$

$$68.2\ =\frac{120\times7y+80\times5y}{200}$$

y = 11

Average weight of the woman employees = 5y

= $$5\times11$$

= 55 kg