Question

X and Y are partners. They share profits and losses in the ratio of \(2:1\). They admit Z by giving him \(\tfrac{1}{4}\) share in future profits. Calculate the new profit-sharing ratio.

Hint:

When a newcomer’s fraction is given and no sacrifice pattern is specified, share the remainder among old partners in the \emph{old ratio}.

Answer 1

Step 1: Understand the allocation.
Z’s share is fixed at \(1/4\). Unless stated otherwise, the remaining \(3/4\) is shared by old partners in their old ratio \(2:1\).
Step 2: Compute each partner’s new share.
Remaining share \(= 1 - \frac{1}{4} = \frac{3}{4}\). \[ X = \frac{3}{4}\times \frac{2}{3}=\frac{1}{2},\quad Y = \frac{3}{4}\times \frac{1}{3}=\frac{1}{4},\quad Z = \frac{1}{4}. \]
Step 3: Convert to simple ratio.
\(\frac{1}{2}:\frac{1}{4}:\frac{1}{4} = 2:1:1\).
Final Answer: \[ \boxed{X:Y:Z = 2:1:1} \] % Quciktip