Partners S and T have capitals ₹90,000 and ₹110,000 respectively with a profit‑sharing ratio of 3:2. After four years, Partner U joins with capital ₹60,000 and will receive interest at 9% per annum for 6 months before admission. After admission the profit‑sharing ratio becomes S : T : U = 4 : 3 : 3. The partnership makes a profit of ₹150,000 during the year of admission. Determine (i) the interest payable to U, (ii) the profit share of each partner after admission, and (iii) the change in profit‑sharing percentages for each partner compared to the original partnership.

Step-by-step solution

1. Interest to U for 6 months at 9%: $60,000\times 0.09\times \frac{6}{12}=2,700$ rupees. Subtract interest from total profit: $150,000-2,700=147,300$ rupees. New ratio parts = 4+3+3=10. S’s share = $\frac{4}{10}\times 147,300=58,920$. T’s share = $\frac{3}{10}\times 147,300=44,190$. U’s share = $\frac{3}{10}\times 147,300=44,190$. Compute original shares (profit 150,000): S = $\frac{3}{5}\times 150,000=90,000$; T = $\frac{2}{5}\times 150,000=60,000$. Percentage change for S: $(58,920-90,000)/90,000\times 100=-34.53$. For T: $(44,190-60,000)/60,000\times 100=-26.35$. U increased from 0 to 44,190, i.e., +100% relative to zero.
2. Answer: Interest ₹2,700; Shares – S ₹58,920, T ₹44,190, U ₹44,190; Changes – S –34.53%, T –26.35%, U +100%

Concept tested: Interest, profit sharing and percentage change on admission

Published 4 October 2026 · How this solution was prepared and checked