Question

X, Y, and Z are partners in 2:1:1 ratio. Y retires. Calculate the new ratio.

Hint:

When a partner retires, the remaining partners share their capital and profits based on their original ratio.

Answer 1

Step 1: Understand the Old Ratio.
The old ratio between X, Y, and Z is 2:1:1.
Step 2: Calculate Y’s share.
Y's share in the profit or capital is given by the formula: \[ \text{Y's Share} = \frac{1}{2+1+1} = \frac{1}{4} \]
Step 3: Adjust for Y’s Retirement.
When Y retires, their share of the capital is either paid out or adjusted between the remaining partners (X and Z). X and Z will share Y's share in the same ratio as their original share ratio (2:1).
Step 4: Calculate the New Ratio.
The total remaining share for X and Z after Y’s retirement will be \( \frac{3}{4} \). To calculate their new ratio: \[ X's \, \text{new share} = 2 \times \frac{1}{3} = \frac{2}{3} \] \[ Z's \, \text{new share} = 1 \times \frac{1}{3} = \frac{1}{3} \] Thus, the new ratio between X and Z is 2:1.