In a certain office, 1/3 of the workers are women, 1/2 of the women are married and 1/3 of the married women have children. If 3/4 of the men are married and 2/3 of the married men have children, then what part of workers are without children?

Let the total number of workers in the office be $$900x$$

=> No. of women = $$\frac{900x}{3} = 300x$$

No. of married woman = $$\frac{300x}{2} = 150x$$

No. of married woman having children = $$\frac{150x}{3} = 50x$$

=> No. of women NOT having children = $$300x - 50x = 250x$$

No. of men = $$900x-300x = 600x$$

No. of married men = $$\frac{3}{4} * 600x = 450x$$

No. of married men having children = $$\frac{2}{3} * 450x = 300x$$

=> No. of men NOT havin children = $$600x - 300x = 300x$$

Now, total no. of workers not having children = $$250x + 300x = 550x$$

$$\therefore$$ Fraction of people without children = $$\frac{550x}{900x} = \frac{11}{18}$$