In a company $$\frac{2}{3}$$ of the workers are girls, $$\frac{1}{2}$$ of the girls are married and $$\frac{1}{3}$$ of the married girls live in hostel. If $$\frac{3}{4}$$ of the boys are married and $$\frac{2}{3}$$ of married boys live in hostel. Calculate the part of workers who don’t live in hostel.

Let total number of employees in the company = $$900x$$

Total number of girls = $$\frac{2}{3}\times900x=600x$$

Similarly, total number of boys = $$900x-600x=300x$$

Married girls = $$\frac{1}{2}\times600x=300x$$

Married girls who lived in hostel = $$\frac{1}{3}\times300x=100x$$

=> Girls who did not live in hostel = $$600x-100x=500x$$

Married boys = $$\frac{3}{4}\times300x=225x$$

Married boys who lived in hostel = $$\frac{2}{3}\times225x=150x$$

=> Boys who did not live in hostel = $$300x-150x=150x$$

$$\therefore$$ Part of workers who don’t live in hostel = $$\frac{(500x+150x)}{900x}$$

= $$\frac{650}{900}=\frac{13}{18}$$

=> Ans - (D)