New Profit Sharing Ratio Questions

$A$, $B$ and $C$ are partners in a firm sharing profits in the ratio of $4:3:2$. They admit $D$ as a new partner. $A$, $B$ and $C$ each surrendered $\frac{1}{3}\text{rd}$ of their shares in favour of $D$. Calculate the new profit sharing ratio of $A$, $B$, $C$ and $D$.

$P$ and $Q$ were partners sharing profits in the ratio of $3:2$. They admit $R$ and $S$ as new partners. $P$ surrenders $\frac{1}{3}\text{rd}$ of his share in favour of $R$ and $Q$ surrenders $\frac{1}{4}\text{th}$ of his share in favour of $S$. Calculate the new profit sharing ratio of $P$, $Q$, $R$ and $S$.

$A$ and $B$ are partners sharing profits in the ratio of $7:5$. They agree to admit $C$, their manager, into partnership, who is to get $\frac{1}{6}\text{th}$ share in profits. He acquires his share as $\frac{1}{24}\text{th}$ from $A$ and $\frac{1}{8}\text{th}$ from $B$. Calculate the new profit sharing ratio.

$A$ 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 in partnership sharing profits and losses in the ratio of $3:2$. They admit $C$ as a new partner. Calculate the new profit sharing ratio if $C$ purchases $\frac{1}{10}\text{th}$ share from $A$.

$A$ and $B$ are partners in a firm sharing profits and losses in the ratio of $5:3$. They admit $C$ as a partner for $\frac{1}{4}\text{th}$ share in the profits of the firm. Calculate the new profit sharing ratio of $A$, $B$ and $C$ if $C$ acquires his share as $\frac{1}{5}\text{th}$ from $A$ and $\frac{1}{20}\text{th}$ from $B$.

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