The graph above shows the distribution of three different flavors of hard candies-cherry, lemon and lime - in a candy jar. If all the lemon candies are removed and no other candies are added or removed, what fraction of the remaining candies in the jar will be lime candies?

(Fraction)

Given, women = $\frac{1}{3}$

Men = $1-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}$

Married women = $\frac{1}{3}of\frac{1}{2}=\frac{1}{6}$ of whole office is married women.

Married women who have children = $\frac{1}{6}of\frac{1}{3}=\frac{1}{18}$ 

Married men= $\frac{2}{3}of\frac{3}{4}=\frac{1}{2}$ of whole workers

Married men who have children = $\frac{1}{2}of\frac{2}{3}=\frac{1}{3}$ of married men. 

Married workers who have children = $\left(\frac{1}{18}+\frac{1}{3}\right)=\frac{1+6}{18}=\frac{7}{18}$ Part of whole workers

$\left(1-\frac{7}{18}\right)=\frac{18-7}{18}=\frac{11}{18}$ Worker does not have children. ans.

Balance = 20,00,000

To wife = (2/5)*20,00,000 = 8,00,000

Remain =20,00,000-8,00,000=12,00,000

To son = (¼)*12,00,000 = 3,00,000

Remain 12,00,00-3,00,000 = 9,00,000

Donated = (2/9)* 9,00,000 = 2,00,000 (Ans.)

$\frac{1}{2}\times \frac{1}{4}\times \frac{1}{8} = \frac{1\times 1\times 1}{2\times 4\times 8}=\frac{1}{64}$