X and Y are partners in a firm with capital of ₹ 18,000 and ₹ 20,000. Z brings ₹ 10,000 for his share of goodwill, and he is required to bring proportionate capital for 1/3rd share in profits. The capital contribution of Z will be ______.

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X and Y are partners in a firm with capital of ₹ 18,000 and ₹ 20,000. Z brings ₹ 10,000 for his share of goodwill, and he is required to bring proportionate capital for $\frac{1}{3}$rd share in profits. The capital contribution of Z will be ₹ 24,000. Explanation: Determine the Sacrificing Ratio and Adjust Capitals for Goodwill: The initial profit-sharing ratio of X and Y is not specified, so we assume they share profits equally. Z brings ₹ 10,000 as goodwill premium. X’s share of goodwill = 10,000 xx $\frac{1}{2}$ = 5,000 Y’s share of goodwill = 10,000 xx $\frac{1}{2}$ = 5,000 The partners’ capitals are adjusted to include their share of the goodwill: X’s adjusted capital = 18,000 + 5,000 = 23,000 Y’s adjusted capital = 20,000 + 5,000 = 25,000 The combined adjusted capital of X and Y = 23,000 + 25,000 = 48,000 Calculate the Total Capital of the New Firm: Remaining Share of X and Y = 1 - $\frac{1}{3}$ = $\frac{2}{3}$ Total Capital of New Firm = 48,000 xx $\frac{3}{2}$ = 72,000 Z is required to bring capital proportionate to his $\frac{1}{3}$rd share in the total capital of the firm, ₹ 72,000 Z’s Capital = 72,000 xx $\frac{1}{3}$ = 24,000

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