Four children $A, B, C$ and $D$ divide a bag of sweets. $A$ takes $\frac{1}{3}$ of them, $B \frac{2}{5}$ th of the remainder and the rest is equally shared between $C$ and $D$. What fraction of the sweets did $C$ or $D$ get?
(a)$\frac{1}{4}$
(b)$\frac{1}{5}$
(c)$\frac{1}{6}$
(d)$\frac{1}{17}$
Answer
Answer (as printed): B
Explanation
A's share $=\frac{1}{3}$. Remainder $=\left(1-\frac{1}{3}\right)=\frac{2}{3}$. B's share $=\frac{2}{5}$ of $\frac{2}{3}=\frac{4}{15}$. Rest $=\left(\frac{2}{3}-\frac{4}{15}\right)=\frac{6}{15}=\frac{2}{5}$. C's share = D's share $=\frac{1}{2}$ of $\frac{2}{5}=\frac{1}{5}$.
Explanation as extracted from the printed page; notation may be imperfect.