Partnership Profit with a Loan
Three friends, Asha, Bina, and Chetan, start a catering business. Asha invests ₹1,20,000 at the start. Bina invests ₹90,000 four months later. Chetan invests ₹1,20,000 six months after the start. The business also takes a loan of ₹60,000 at 10% simple interest per annum for six months; the interest is paid from the business's earnings before profit is shared. At the end of the first year, total revenue is ₹4,80,000 and operating expenses are ₹1,80,000. Profits are shared in proportion to capital contributed multiplied by the time it remained invested. The partners want to know each one's share, and Chetan asks how his share would change if he had invested at the start instead of after six months, with all other facts unchanged. They also want to know the minimum revenue needed for Asha's share to be at least ₹1,60,000.
1. Calculate each partner's share of the year-end profit.
Read the worked answer
Gross profit before loan interest = ₹4,80,000 − ₹1,80,000 = ₹3,00,000. Loan interest = ₹60,000 × 10% × 6/12 = ₹3,000. Distributable profit = ₹2,97,000. Capital-months: Asha ₹1,20,000×12 = ₹14,40,000; Bina ₹90,000×8 = ₹7,20,000; Chetan ₹1,20,000×6 = ₹7,20,000. Ratio = 14,40,000:7,20,000:7,20,000 = 2:1:1. Total parts = 4. Asha = 2,97,000×2/4 = ₹1,48,500; Bina = ₹74,250; Chetan = ₹74,250. Check: 1,48,500+74,250+74,250 = ₹2,97,000.
2. How would Chetan's share change if he had invested at the start instead of after six months, all else unchanged?
Read the worked answer
Chetan's capital-month would become ₹1,20,000×12 = ₹14,40,000. Ratio = 14,40,000:7,20,000:14,40,000 = 2:1:2, total 5 parts. Distributable profit is still ₹2,97,000, so one part = ₹59,400. Asha = ₹1,18,800; Bina = ₹59,400; Chetan = ₹1,18,800. Chetan's share rises from ₹74,250 to ₹1,18,800, an increase of ₹44,550. Asha's share falls by ₹29,700 because the same profit is now split over five parts rather than four, and Chetan holds two of them.
3. What minimum total revenue would give Asha at least ₹1,60,000 under the original timing?
Read the worked answer
Under the original 2:1:1 ratio, Asha receives half of distributable profit. Let net distributable profit be N; Asha = N/2 ≥ ₹1,60,000, so N ≥ ₹3,20,000. Gross profit must be N + interest = ₹3,20,000 + ₹3,000 = ₹3,23,000. Revenue = gross profit + operating expenses = ₹3,23,000 + ₹1,80,000 = ₹5,03,000. So minimum revenue is ₹5,03,000, assuming costs and interest stay unchanged.