WBCS Mains 2019 Official Paper-VI

$A$ and $B$ are equal partners. They admit $C$ and $D$ as partners with $\frac{1}{5}\text{th}$ and $\frac{1}{6}\text{th}$ share respectively. What is the profit sharing ratio of all the partners?

$A$ and $B$ are partners sharing profits in the ratio of $7:3$. They admit $C$ for $\frac{1}{5}\text{th}$ share, which he acquires in equal proportions from both. Find the new profit sharing ratio.

$A$ and $B$ are partners sharing profits in the ratio of $5:4$. They admit $C$ for $\frac{1}{9}\text{th}$ share, which he acquires entirely from $A$. Find out the new profit sharing ratio.

$X$ and $Y$ are partners in a firm sharing profits in the ratio of $3:2$. They admit $R$ as a new partner. $X$ gives $\frac{1}{3}\text{rd}$ of his share while $Y$ gives $\frac{1}{10}\text{th}$ from his share. Calculate the sacrificing ratio.

$P$ and $Q$ are partners sharing profits in the ratio of $3:2$. $P$ surrenders $\frac{1}{6}\text{th}$ of his share and $Q$ surrenders $\frac{1}{4}\text{th}$ of his share in favour of $R$, a new partner. What is the sacrificing ratio?