Partnership is an important topic in quantitative aptitude. Questions from this chapter are common in SSC, Banking, Railway, CAT, placement tests, and other competitive exams. The idea is simple: when two or more people invest money in a business, the profit or loss is divided according to their investment and the time for which the money remains in the business.
A partnership is a business arrangement in which two or more people agree to work together, invest money, or share responsibility. In aptitude questions, we mainly focus on how profit or loss is divided among partners. If all partners invest for the same time, profit is divided in the ratio of their investments. If they invest for different time periods, profit is divided in the ratio of capital multiplied by time.
This lesson explains partnership in simple language with formulas, cases, working partner and sleeping partner examples, changing investment questions, shortcuts, solved examples, practice questions, and FAQs.
What Is Partnership?
When two or more persons start a business jointly, they are called partners and the business relation is called partnership. The money invested by a partner is called capital. The gain from business is called profit, and the loss from business is called loss.
Example: A and B start a shop. A invests Rs. 20000 and B invests Rs. 30000. Both are partners. If the business earns profit, that profit will be shared according to the agreed rule. In aptitude questions, the usual rule is investment ratio or investment × time ratio.
Important Terms in Partnership
| Term | Meaning |
|---|---|
| Partner | A person who joins the business |
| Capital | Money invested in the business |
| Profit | Gain from the business |
| Loss | Money lost in the business |
| Profit ratio | Ratio in which profit is divided |
| Working partner | Partner who invests and also manages the business |
| Sleeping partner | Partner who only invests money |
Existing Explanation
Partnership
When two or more than two persons are a business jointly they are called partners & the deal is known as partnership.
Ratio of division of gain.
When investments of all the partner are for the same time the gain or loss is distributed among the partners in the ratio of their investment A’s share of profit: B’s share of profit.
When investments are for different time periods then equivalent capital are calculated for unit of time by taking (capital × numbers of units of time) now gain or loss is divided in the ratio of these capitals.
A invest of Rs x for p month & B invest Rs y for q month.
Then profit distributed in xp : yq
Working & sleeping partner
A partner who manages the business is known as working partner & the one who simply invests the money is a sleeping partner.
Basic Rule of Partnership
If all partners invest their money for the same time period, the profit or loss is divided in the ratio of their investments.
A’s share : B’s share = A’s investment : B’s investment.
Example: A invests Rs. 40000 and B invests Rs. 60000 for one year. Profit is Rs. 20000. Find their shares.
Investment ratio = 40000 : 60000 = 2 : 3.
Total ratio parts = 2 + 3 = 5.
A’s share = 2/5 × 20000 = Rs. 8000.
B’s share = 3/5 × 20000 = Rs. 12000.
Capital × Time Rule
If partners invest money for different time periods, we calculate equivalent capital by multiplying investment with time.
Profit ratio = capital × time.
If A invests Rs. x for p months and B invests Rs. y for q months, then:
A’s share : B’s share = xp : yq.
Example: A invests Rs. 5000 for 12 months and B invests Rs. 8000 for 6 months. Find the profit ratio.
A’s equivalent capital = 5000 × 12 = 60000.
B’s equivalent capital = 8000 × 6 = 48000.
Ratio = 60000 : 48000 = 5 : 4.
So profit will be divided in the ratio 5 : 4.
Working Partner and Sleeping Partner
A working partner is a partner who manages the business. A sleeping partner invests money but does not take part in daily business work.
In many questions, the working partner first receives a fixed salary or a fixed percentage of profit for managing the business. The remaining profit is then divided according to investment ratio.
Example: A is a working partner and B is a sleeping partner. A invests Rs. 30000 and B invests Rs. 50000. Total profit is Rs. 10000. A gets 20 percent of profit for managing the business. The remaining profit is divided according to capital. Find B’s share.
A’s working commission = 20 percent of 10000 = Rs. 2000.
Remaining profit = 10000 – 2000 = Rs. 8000.
Capital ratio A : B = 30000 : 50000 = 3 : 5.
B’s share from remaining profit = 5/8 × 8000 = Rs. 5000.
So B gets Rs. 5000.
Types of Partnership Questions
- Same investment period questions
- Different investment period questions
- Changing capital during the year
- Admission of a new partner
- Withdrawal of capital by a partner
- Working partner and sleeping partner questions
- Finding total profit from one partner’s share
- Finding investment from profit ratio
Case 1: Same Time Investment
Question: A and B invest Rs. 12000 and Rs. 18000 respectively for the same time. If the profit is Rs. 10000, find B’s share.
Investment ratio = 12000 : 18000 = 2 : 3.
Total parts = 5.
B’s share = 3/5 × 10000 = Rs. 6000.
Case 2: Different Time Investment
Question: A invests Rs. 10000 for 8 months and B invests Rs. 12000 for 6 months. Find the profit ratio.
A’s equivalent investment = 10000 × 8 = 80000.
B’s equivalent investment = 12000 × 6 = 72000.
Ratio = 80000 : 72000 = 10 : 9.
So profit ratio is 10 : 9.
Case 3: New Partner Joins Later
Question: A starts a business with Rs. 15000. After 4 months, B joins with Rs. 20000. At the end of one year, profit is Rs. 22000. Find their shares.
A’s money remains for 12 months.
B’s money remains for 8 months.
A’s equivalent capital = 15000 × 12 = 180000.
B’s equivalent capital = 20000 × 8 = 160000.
Profit ratio = 180000 : 160000 = 9 : 8.
Total parts = 17.
A’s share = 9/17 × 22000 = Rs. 11647.06 approximately.
B’s share = 8/17 × 22000 = Rs. 10352.94 approximately.
Case 4: Partner Withdraws Capital
Question: A and B start a business. A invests Rs. 24000 and B invests Rs. 30000. After 6 months, A withdraws Rs. 6000. Find the profit ratio at the end of one year.
A invests Rs. 24000 for first 6 months and Rs. 18000 for next 6 months.
A’s equivalent capital = 24000 × 6 + 18000 × 6 = 144000 + 108000 = 252000.
B invests Rs. 30000 for 12 months.
B’s equivalent capital = 30000 × 12 = 360000.
Profit ratio = 252000 : 360000 = 7 : 10.
Case 5: Partner Adds More Capital
Question: A invests Rs. 20000 and B invests Rs. 25000. After 4 months, A adds Rs. 10000 more. Find the profit ratio after one year.
A invests Rs. 20000 for 4 months and Rs. 30000 for 8 months.
A’s equivalent capital = 20000 × 4 + 30000 × 8 = 80000 + 240000 = 320000.
B invests Rs. 25000 for 12 months.
B’s equivalent capital = 25000 × 12 = 300000.
Profit ratio = 320000 : 300000 = 16 : 15.
How to Find Total Profit
If one partner’s share and profit ratio are given, total profit can be found using ratio parts.
Example: A and B share profit in the ratio 3 : 5. B’s share is Rs. 15000. Find total profit.
5 parts = 15000.
1 part = 3000.
Total parts = 3 + 5 = 8.
Total profit = 8 × 3000 = Rs. 24000.
How to Find Investment from Profit Share
If time is same, investment ratio is same as profit ratio.
Example: A and B share profit in the ratio 4 : 7. A invests Rs. 20000. Find B’s investment if time is same.
A : B = 4 : 7.
4 parts = 20000.
1 part = 5000.
B’s investment = 7 × 5000 = Rs. 35000.
Worked Examples
Example 1
A and B invest Rs. 50000 and Rs. 75000 for the same time. Profit is Rs. 30000. Find A’s share.
Ratio = 50000 : 75000 = 2 : 3.
A’s share = 2/5 × 30000 = Rs. 12000.
Example 2
A invests Rs. 6000 for 10 months and B invests Rs. 9000 for 8 months. Find profit ratio.
A = 6000 × 10 = 60000.
B = 9000 × 8 = 72000.
Ratio = 5 : 6.
Example 3
A, B, and C invest Rs. 10000, Rs. 15000, and Rs. 20000 for the same time. Profit is Rs. 9000. Find C’s share.
Ratio = 10000 : 15000 : 20000 = 2 : 3 : 4.
Total parts = 9.
C’s share = 4/9 × 9000 = Rs. 4000.
Example 4
A invests Rs. 12000 for 12 months, B invests Rs. 16000 for 9 months, and C invests Rs. 20000 for 6 months. Find the profit ratio.
A = 12000 × 12 = 144000.
B = 16000 × 9 = 144000.
C = 20000 × 6 = 120000.
Ratio = 144000 : 144000 : 120000 = 6 : 6 : 5.
Shortcut Method
In partnership questions, do not directly compare only investment unless the time is same. Always compare investment × time.
For example, Rs. 10000 for 12 months is equal to Rs. 20000 for 6 months because both give 120000 as equivalent capital.
This idea saves time in exams.
Common Mistakes
- Dividing profit only according to capital when time periods are different.
- Forgetting to subtract working partner salary or commission before dividing remaining profit.
- Counting months incorrectly when a partner joins later.
- Ignoring capital withdrawn or added during the year.
- Using total profit as one partner’s share.
- Not simplifying the ratio before calculating shares.
Practice Questions
- A and B invest Rs. 40000 and Rs. 60000 for same time. Profit is Rs. 25000. Find A’s share.
- A invests Rs. 5000 for 12 months and B invests Rs. 8000 for 9 months. Find profit ratio.
- A starts business with Rs. 20000. B joins after 3 months with Rs. 30000. Find profit ratio after one year.
- A and B share profit in ratio 5 : 7. Total profit is Rs. 36000. Find B’s share.
- A’s share is Rs. 9000 in ratio 3 : 4. Find total profit.
- A invests Rs. 24000 for 8 months and B invests Rs. 16000 for 12 months. Find ratio.
- A is working partner and gets 10 percent of Rs. 50000 profit. Remaining profit is divided between A and B in ratio 2 : 3. Find B’s share.
- A invests Rs. 10000. After 6 months he adds Rs. 5000. Find his equivalent capital for one year.
Answers to Practice Questions
- Rs. 10000.
- Ratio = 5 : 6.
- A : B = 8 : 9.
- Rs. 21000.
- Rs. 21000.
- Ratio = 1 : 1.
- Remaining profit = Rs. 45000. B’s share = 3/5 × 45000 = Rs. 27000.
- Equivalent capital = 10000 × 6 + 15000 × 6 = 150000.
Frequently Asked Questions
What is partnership in aptitude?
Partnership is a topic where two or more persons invest money in a business and profit or loss is shared according to investment and time.
What is the basic formula of partnership?
If time is different, profit ratio = capital × time.
What is a working partner?
A working partner is a partner who manages the business and may receive salary or commission before profit sharing.
What is a sleeping partner?
A sleeping partner only invests money and does not manage daily business work.
When is profit divided only by investment ratio?
Profit is divided by investment ratio when all partners invest for the same time period.
What happens if a partner joins late?
His capital is counted only for the months it remains in the business.
What happens if capital changes during the year?
Calculate capital × time separately for each period and add them.
Advanced Partnership Examples
Example 1: Three Partners with Different Time
A, B, and C invest Rs. 10000, Rs. 12000, and Rs. 15000 respectively. A invests for 12 months, B for 10 months, and C for 8 months. Find the ratio of profit.
A’s equivalent capital = 10000 × 12 = 120000.
B’s equivalent capital = 12000 × 10 = 120000.
C’s equivalent capital = 15000 × 8 = 120000.
Profit ratio = 1 : 1 : 1.
Example 2: Finding Investment
A and B start a business. A invests Rs. 36000 for 10 months and B invests some amount for 12 months. If their profit ratio is 5 : 4, find B’s investment.
A’s equivalent capital = 36000 × 10 = 360000.
Let B’s investment be x.
B’s equivalent capital = 12x.
360000 : 12x = 5 : 4.
360000/12x = 5/4.
1440000 = 60x.
x = 24000.
So B invested Rs. 24000.
Example 3: Finding Time
A invests Rs. 20000 for 12 months. B invests Rs. 30000. If profit ratio is 4 : 3, find for how many months B invested.
A’s equivalent capital = 20000 × 12 = 240000.
Let B invests for x months.
B’s equivalent capital = 30000x.
240000 : 30000x = 4 : 3.
240000/30000x = 4/3.
720000 = 120000x.
x = 6.
So B invested for 6 months.
Example 4: Salary to Working Partner
A and B invest Rs. 40000 and Rs. 60000. A is a working partner and gets Rs. 5000 salary from total profit. Total profit is Rs. 30000. Find B’s share.
First give salary to A.
Remaining profit = 30000 – 5000 = Rs. 25000.
Investment ratio = 40000 : 60000 = 2 : 3.
B’s share = 3/5 × 25000 = Rs. 15000.
Example 5: Profit and Loss
A and B invest in the ratio 7 : 5. If the business has a loss of Rs. 24000, find A’s loss.
Total parts = 7 + 5 = 12.
A’s loss = 7/12 × 24000 = Rs. 14000.
Partnership and Ratio Connection
Partnership questions are mostly ratio questions. The ratio may come directly from investment, or it may come from investment multiplied by time. Once the correct ratio is found, the remaining calculation is simple.
If total profit is given, divide it according to the ratio. If one partner’s share is given, first find the value of one ratio part and then calculate the required value. If investment or time is missing, make an equation using equivalent capital.
Step-by-Step Method for Any Partnership Question
- Write each partner’s investment.
- Write the time for which each investment remained in business.
- If investment changes, split the time into parts.
- Calculate capital × time for every partner.
- Simplify the ratio.
- If there is working salary or commission, subtract it first.
- Divide the remaining profit or loss according to the ratio.
Government Exam Style Questions
Question 1
A and B invest in the ratio 3 : 4. If total profit is Rs. 28000, find A’s share.
A’s share = 3/7 × 28000 = Rs. 12000.
Question 2
A invests Rs. 25000 for 9 months and B invests Rs. 30000 for 6 months. Find profit ratio.
A = 25000 × 9 = 225000.
B = 30000 × 6 = 180000.
Ratio = 5 : 4.
Question 3
A starts a business with Rs. 50000. After 6 months B joins with Rs. 80000. Profit at the end of year is Rs. 42000. Find B’s share.
A = 50000 × 12 = 600000.
B = 80000 × 6 = 480000.
Ratio = 5 : 4.
B’s share = 4/9 × 42000 = Rs. 18666.67 approximately.
One-Minute Revision
If all partners invest for the same time, compare only capital. If time is different, compare capital × time. If a partner joins late, count only the remaining months. If a partner withdraws or adds money, calculate each period separately.
For working partners, salary or commission is usually taken out of total profit first. The remaining profit is divided according to the final ratio. This one point is very important in SSC and Banking questions.
More Practice for Accuracy
Question: A, B, and C invest Rs. 15000, Rs. 20000, and Rs. 25000 for the same time. If profit is Rs. 24000, find C’s share.
Investment ratio = 15000 : 20000 : 25000 = 3 : 4 : 5.
Total parts = 12.
C’s share = 5/12 × 24000 = Rs. 10000.
Question: A invests Rs. 18000 for 8 months and B invests Rs. 24000 for 6 months. If total profit is Rs. 20000, find A’s share.
A’s equivalent capital = 18000 × 8 = 144000.
B’s equivalent capital = 24000 × 6 = 144000.
Ratio = 1 : 1.
A’s share = Rs. 10000.
Question: A and B invest in ratio 2 : 5. B receives Rs. 15000 profit. Find A’s share.
5 parts = 15000, so 1 part = 3000.
A’s share = 2 parts = Rs. 6000.
These examples show that the calculation is not difficult if the ratio is correct. In partnership, the main work is to identify whether time is same or different.
Before answering any partnership question, write the investment and time clearly in a small table. This prevents most mistakes. After finding the profit ratio, always check whether the question asks for total profit, one partner’s share, investment amount, time period, or remaining profit after salary.
For quick revision, remember this core rule: profit follows money multiplied by time.
Conclusion
Partnership questions are mainly ratio questions. If time is same, compare investments. If time is different, compare investment multiplied by time.
Read the question carefully, calculate equivalent capital correctly, and then divide profit according to the final ratio.