Partnership • Topic 1 of 3

Investment Ratio

The first job in any partnership problem is to build the correct investment ratio, because every later step just scales this ratio. When all partners invest for the same length of time, the ratio is simply the ratio of their capitals: ₹30,000 and ₹45,000 give 30 : 45 = 2 : 3. But when partners join at different times or withdraw early, you must weight each capital by the months it actually worked — this is the capital-month (rupees × months). A partner who puts in ₹20,000 for 12 months and one who puts in ₹40,000 for only 6 months both contribute 2,40,000 money-months, so they split equally despite unequal cash. The CAT-smart move is to cancel common factors immediately — divide every capital-month by their GCD before you touch the profit. Always reduce ratios to lowest terms; clean integers make the final division instant.

✅ Solved examples

1. A invests ₹25,000 and B invests ₹35,000 for the same period. Find the profit-sharing ratio.
Same time, so ratio = capitals = 25000 : 35000 = 5 : 7.
2. P puts in ₹12,000 for 8 months and Q puts in ₹9,000 for 12 months. Find their ratio.
Capital-months: P = 12000×8 = 96000; Q = 9000×12 = 108000. Ratio = 96 : 108 = 8 : 9.
3. X invests ₹40,000 for the whole year; Y invests ₹60,000 but joins after 4 months. Find the ratio.
X = 40000×12 = 4,80,000; Y = 60000×8 = 4,80,000. Ratio = 1 : 1.
4. A invests ₹50,000 for 12 months but withdraws ₹20,000 after 6 months. Find A’s total capital-months.
First 6 months: 50000×6 = 3,00,000. Last 6 months at ₹30,000: 30000×6 = 1,80,000. Total = 4,80,000 capital-months.

✏️ Practice — try these, take hints as needed

1. A invests ₹18,000 and B ₹24,000 for equal time. Profit ratio?
Equal time ⇒ ratio of capitals.
18000 : 24000.
Cancel by 6000.
3 : 4
2. M invests ₹15,000 for 10 months, N ₹25,000 for 6 months. Ratio?
Use rupees × months.
M = 1,50,000; N = 1,50,000.
Compare.
1 : 1
3. A: ₹8,000 for 12 months; B: ₹12,000 for 8 months; C: ₹16,000 for 6 months. Ratio?
Capital-months each.
96000 : 96000 : 96000.
All equal.
1 : 1 : 1
4. P invests ₹30,000, doubles it to ₹60,000 after 8 months. Total capital-months for the year?
Phase 1: 30000×8.
Phase 2: 60000×4.
Add the two.
4,80,000
5. A: ₹20,000 for 12 months; B joins after 3 months with ₹25,000. Ratio of A : B?
A for 12, B for 9 months.
A = 2,40,000; B = 2,25,000.
Cancel by 15,000.
16 : 15

📝 Topic test — 8 questions

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