Q.X and Y share profits in the ratio 3:2. On admission of Z for 1/5 share, it is agreed that the capitals of all partners shall be made proportionate to the new profit-sharing ratio, on the basis of Z's own capital. Z brings in ₹50,000 as his capital for his 1/5 share. After adjusting for revaluation and goodwill, the capitals of X and Y stand at ₹1,60,000 and ₹1,10,000 respectively. Calculate the new required capital of each partner and the amount to be brought in or withdrawn by X and Y.

Z's ₹50,000 for a 1/5 share fixes the whole firm's capital at ₹2,50,000; each partner's required capital is then his own share of that total, compared against his existing adjusted capital.

Since Z's ₹50,000 represents his 1/5 share, the total capital of the reconstituted firm is found by grossing this up:

Total Capital of New Firm = Z's Capital ÷ Z's Share = 50,000 ÷ (1/5) = 50,000 × 5 = ₹2,50,000.

New profit-sharing ratio: Z takes 1/5, leaving 4/5 to be shared by X and Y in their old ratio 3:2 — X = 4/5 × 3/5 = 12/25, Y = 4/5 × 2/5 = 8/25, Z = 5/25. New ratio X : Y : Z = 12 : 8 : 5 (out of 25).

Required capital of each partner = Total Capital × his new share:

X: 2,50,000 × 12/25 = ₹1,20,000

Y: 2,50,000 × 8/25 = ₹80,000

Z: 2,50,000 × 5/25 = ₹50,000 (matches the capital Z actually brought in, as it should)

Check: 1,20,000 + 80,000 + 50,000 = 2,50,000, exactly the total capital computed above.

Comparing each old partner's ADJUSTED capital (already given, after revaluation and goodwill) against his required capital:

X: adjusted ₹1,60,000 vs required ₹1,20,000 → excess of ₹40,000, to be WITHDRAWN.

Y: adjusted ₹1,10,000 vs required ₹80,000 → excess of ₹30,000, to be WITHDRAWN. …

A common mistake is dividing Z's ₹50,000 directly among X and Y in the new ratio to find their required capitals, instead of first grossing up Z's capital by his OWN share (1/5) to find the firm's TOTAL capital …