Question

X, Y and Z are partners sharing profits in the ratio \(3:2:2\). Z retires. X and Y decide to share future profits in the ratio \(4:3\). Calculate the \emph{gaining ratio}.

Hint:

Gaining ratio is always for \emph{continuing} partners: \( \text{New} - \text{Old} \).

Answer 1

Step 1: Find old shares.
Old ratio \(3:2:2\) ⇒ \(X=\frac{3}{7},\ Y=\frac{2}{7},\ Z=\frac{2}{7}\).
Step 2: Note new shares of continuing partners.
New ratio \(4:3\) ⇒ \(X=\frac{4}{7},\ Y=\frac{3}{7}\).
Step 3: Compute gains (New − Old).
\(X\)’s gain \(= \frac{4}{7}-\frac{3}{7}=\frac{1}{7}\). \(Y\)’s gain \(= \frac{3}{7}-\frac{2}{7}=\frac{1}{7}\).
Step 4: Express as a ratio.
\(X:Y = \frac{1}{7}:\frac{1}{7} = 1:1\).
Final Answer: \[ \boxed{\text{Gaining Ratio } X:Y = 1:1} \] % Quciktip