5.3A Three-Partner Compound Partnership

Example 35B: A, B and C invest ₹20,000, ₹30,000, and ₹40,000 respectively. A invests for the full year, B invests for 8 months, and C invests for 6 months. If the total profit is ₹18,000, find each partner’s share. A’s capital-months = 20,000 × 12 = 240,000 B’s capital-months = 30,000 × 8 = 240,000 C’s capital-months = 40,000 × 6 = 240,000 All three are equal, so the ratio is 1 : 1 : 1, and the profit is split equally. Each partner’s share = 18,000 / 3 = ₹6,000. (This example is a good reminder that a compound partnership ratio does not always favour the partner with the largest raw investment — a shorter duration can fully offset a larger capital amount, as seen here where all three effective contributions turned out equal.)

Example 35C (three-partner compound partnership with staggered mid-year entry, additional): A starts a business with ₹24,000. After 3 months, B joins with ₹36,000. After 8 months from the start, C joins with ₹90,000. At the end of the year, the total profit is ₹54,000. Find each partner’s share. A’s capital-months = 24,000 × 12 = 288,000 B’s capital-months = 36,000 × (12 − 3) = 36,000 × 9 = 324,000 C’s capital-months = 90,000 × (12 − 8) = 90,000 × 4 = 360,000 Ratio = 288,000 : 324,000 : 360,000. Dividing every term by 36,000: 8 : 9 : 10, total parts = 27. Value of 1 part = 54,000/27 = 2,000. A’s share = 8 × 2,000 = ₹16,000; B’s share = 9 × 2,000 = ₹18,000; C’s share = 10 × 2,000 = ₹20,000. Check: 16,000 + 18,000 + 20,000 = 54,000. ✔

Example 35D (compound partnership with a withdrawal and a new entrant, additional): A invests ₹50,000 for the entire year. B invests ₹60,000 but withdraws ₹20,000 after 6 months (continuing with the reduced amount for the rest of the year). C joins the business after 6 months with ₹40,000. If the total profit at year-end is ₹36,000, find each partner’s share. A’s capital-months = 50,000 × 12 = 600,000 B’s capital-months = (60,000 × 6) + (40,000 × 6) = 360,000 + 240,000 = 600,000 C’s capital-months = 40,000 × 6 = 240,000 Ratio = 600,000 : 600,000 : 240,000. Dividing every term by 120,000: 5 : 5 : 2, total parts = 12. Value of 1 part = 36,000/12 = 3,000. A’s share = 5 × 3,000 = ₹15,000; B’s share = 5 × 3,000 = ₹15,000; C’s share = 2 × 3,000 = ₹6,000. Check: 15,000 + 15,000 + 6,000 = 36,000. ✔