Partnership for IBPS Clerk

Partnership is ratio with a business story around it. Two or three people put money into a business for some months, the business makes a profit, and you have to split it fairly. Every question in this chapter comes down to one ratio. What changes is how much work it takes to build that ratio.

In the clerk exam, partnership turns up as a direct arithmetic question and occasionally inside a DI set, for example a table of each partner's investment and months. It is a scoring topic because the method never changes. The traps are in the reading: a partner who joins late, one who withdraws part of their money, or a salary that has to come out before the split.

The rule, and why it is fair

Profit ratio = capital × time, for each partner.

Think of it as money-months. ₹10,000 kept in the business for 6 months does the same work as ₹60,000 kept for 1 month: both give the business 60,000 rupee-months to use. So a partner's claim on profit is the product of how much they put in and how long it stayed.

• Same time for everyone: the times cancel, and profit ratio = capital ratio.
• Same capital for everyone: profit ratio = time ratio.
• A partner joins after k months in a 12-month year: their time is 12 − k.
• Capital changes midway: split that partner's year into periods and add capital × months for each period.
• A salary or commission for the working partner: take it out of the profit first, then share the rest.

Worked examples

Example 1. A invests ₹20,000 and B invests ₹30,000 for one year. The profit is ₹10,000. Find each share.

1. Same time, so the ratio is 20,000 : 30,000 = 2 : 3.
2. One part = 10,000 ÷ 5 = 2,000. A gets ₹4,000, B gets ₹6,000.

Example 2. A starts a business with ₹50,000. After 4 months, B joins with ₹60,000. The profit at the end of the year is ₹27,000. Find each share.

1. A: 50,000 × 12 = 6,00,000. B was in the business for 8 months: 60,000 × 8 = 4,80,000.
2. Ratio = 5 : 4. One part = 27,000 ÷ 9 = 3,000.
3. A gets ₹15,000, B gets ₹12,000.

Example 3. A starts with ₹40,000 and withdraws ₹10,000 after 6 months. B invests ₹30,000 for the whole year. The year's profit is ₹26,000. Find each share.

1. A: 40,000 × 6 + 30,000 × 6 = 2,40,000 + 1,80,000 = 4,20,000.
2. B: 30,000 × 12 = 3,60,000.
3. Ratio = 42 : 36 = 7 : 6. One part = 26,000 ÷ 13 = 2,000.
4. A gets ₹14,000, B gets ₹12,000.

Example 4. A and B invest ₹60,000 and ₹40,000 for a year. A manages the business and first receives 10% of the profit as a salary. The rest is shared in the capital ratio. The profit is ₹50,000. How much does each get?

1. Salary = 10% of 50,000 = ₹5,000. Remaining = ₹45,000.
2. Capital ratio = 3 : 2. One part = 45,000 ÷ 5 = 9,000, so A gets 27,000 and B gets 18,000.
3. A's total = 27,000 + 5,000 = ₹32,000. B gets ₹18,000.

Example 5. A invests ₹45,000 for the whole year. B joins some months later with ₹30,000. At the end of the year the profit is shared in the ratio 2 : 1. After how many months did B join?

1. Let B stay for t months. 45,000 × 12 : 30,000 × t = 2 : 1.
2. 5,40,000 = 2 × 30,000 × t = 60,000t, so t = 9.
3. B was in for 9 months, so B joined after 3 months.

Example 6. A, B and C invest capitals in the ratio 3 : 4 : 5 for 4, 3 and 2 months respectively. C's share of the profit is ₹5,000. Find the total profit.

1. Products: 3 × 4 : 4 × 3 : 5 × 2 = 12 : 12 : 10 = 6 : 6 : 5.
2. C's 5 parts = 5,000, so one part = 1,000.
3. Total = 17 parts = ₹17,000.

Common mistakes

• Counting "joined after 4 months" as 4 months invested instead of 8.
• Using the capital ratio when the partners stayed for different lengths of time.
• Sharing the whole profit first and adding the salary afterwards, which double-counts it.
• In a withdrawal question, applying the reduced capital to the whole year.
• Forgetting that the year has 12 months when a question says "at the end of the year" but gives some periods in months.

Practice

Set a six-minute timer.

1. A, B and C invest ₹40,000, ₹60,000 and ₹80,000 for a year. The profit is ₹36,000. Find each share.
2. A invests ₹10,000 for 12 months; B invests ₹15,000 for 8 months. The profit is ₹10,000. Find each share.
3. A starts with ₹30,000. After 6 months, B joins with ₹40,000. The year's profit is ₹26,000. Find each share.
4. A and B invest capitals in the ratio 5 : 6 for 8 months and 10 months. The profit is ₹15,000. Find each share.
5. A starts with ₹24,000 and adds ₹6,000 after 3 months. B invests ₹36,000 for the whole year. The profit is ₹43,000. Find each share.
6. A and B invest equal amounts. A is paid ₹1,000 a month for managing the business, and the rest is shared equally. The year's profit is ₹60,000. How much does A get in all?
7. A invests ₹20,000 for 12 months and B invests for 8 months. They share the profit equally. What was B's capital?
8. A, B and C invest capitals in the ratio 2 : 3 : 5 for 6, 4 and 3 months. C gets ₹2,000 more than A. Find the total profit.

Answers:

1. ₹8,000, ₹12,000 and ₹16,000. Ratio 2 : 3 : 4, one part = 36,000 ÷ 9 = 4,000.
2. ₹5,000 each. 1,20,000 : 1,20,000 = 1 : 1.
3. ₹15,600 and ₹10,400. 3,60,000 : 2,40,000 = 3 : 2, one part = 5,200.
4. ₹6,000 and ₹9,000. 5 × 8 : 6 × 10 = 40 : 60 = 2 : 3.
5. ₹19,000 and ₹24,000. A = 24,000 × 3 + 30,000 × 9 = 72,000 + 2,70,000 = 3,42,000. B = 4,32,000. Ratio 19 : 24, one part = 43,000 ÷ 43 = 1,000.
6. ₹36,000. Salary 12 × 1,000 = 12,000. The rest, 48,000, is split 24,000 each. A = 12,000 + 24,000.
7. ₹30,000. 20,000 × 12 = x × 8 gives x = 30,000.
8. ₹26,000. 12 : 12 : 15 = 4 : 4 : 5. C − A = 1 part = 2,000, so the total = 13 parts.

What to do next

• Write the money-months idea in your own words once. It stops you from mixing up capital and time.
• Solve five "joined late" and five "capital changed" questions, writing each partner's periods on separate lines.
• Brush up the parts method in ratio and proportion, which every partnership answer ends with.
• For mixed practice, pair this chapter with profit and loss and word problems.