SSC Partnership Questions with Solutions and Tricks

Partnership is a ratio-based chapter in SSC Quantitative Aptitude. Questions are asked on dividing profit among partners who invest different amounts for different times. With the simple rule "profit is shared in the ratio of capital x time", most questions can be solved in 30 seconds. This practice paper gives you 30 partnership questions with answers and short solutions.

Practice Paper at a Glance

What Is Partnership? Basic Concept in Simple Words

When two or more persons start a business by investing money together, it is called a partnership. The profit or loss is shared among them according to their investments and the time for which each investment stays in the business.

• Active (working) partner manages the business and often gets a salary or commission.
• Sleeping partner only invests money and does not work.
• If the time is the same for everyone, the profit ratio equals the capital ratio. If the capital is the same, the profit ratio equals the time ratio.

Formulas and Shortcut Tricks for SSC Partnership

• Profit ratio = (Capital 1 x Time 1) : (Capital 2 x Time 2) : ...
• Share of a partner = (His ratio part / Sum of ratio parts) x Total profit.
• Equal time: profit ratio = capital ratio. Equal capital: profit ratio = time ratio.
• Joining later: if a partner joins after m months, his time = 12 - m months for a year.
• Working partner: first deduct his salary or commission from the profit, then divide the remaining profit in the ratio of capital x time.
• Fractions of capital: convert 1/2, 1/3, 1/6 into a ratio by taking the LCM (3 : 2 : 1).
• Change in capital: calculate the capital x time for each period separately and add them.
• Difference in share = difference in ratio parts x value of one part.

Set 1: Basic Partnership Questions (Q1–Q10)

Q1. A and B invest Rs 6,000 and Rs 9,000 in a business. If the profit is Rs 3,000, find the share of A.
Answer: Rs 1,200
Solution: Ratio = 6 : 9 = 2 : 3. A = 3,000 x 2/5 = Rs 1,200.

Q2. A, B and C invest Rs 2,000, Rs 3,000 and Rs 5,000. If the profit is Rs 5,000, find the share of C.
Answer: Rs 2,500
Solution: Ratio = 2 : 3 : 5. C = 5,000 x 5/10 = Rs 2,500.

Q3. A invests Rs 5,000 for 12 months and B invests Rs 6,000 for 10 months. Find the ratio of their profits.
Answer: 1 : 1
Solution: A = 5,000 x 12 = 60,000 and B = 6,000 x 10 = 60,000. Ratio = 1 : 1.

Q4. A invests Rs 8,000 for a year and B invests Rs 12,000 for 6 months. If the profit is Rs 7,000, find the share of A.
Answer: Rs 4,000
Solution: A = 8,000 x 12 = 96,000 and B = 12,000 x 6 = 72,000. Ratio = 4 : 3. A = 7,000 x 4/7 = Rs 4,000.

Q5. A and B invest Rs 4,500 and Rs 6,000 for the same period. If the profit is Rs 2,100, find the share of B.
Answer: Rs 1,200
Solution: Ratio = 4,500 : 6,000 = 3 : 4. B = 2,100 x 4/7 = Rs 1,200.

Q6. The capitals of A and B are in the ratio 2 : 3 and their times are in the ratio 3 : 2. Find the ratio of their profits.
Answer: 1 : 1
Solution: Profit ratio = (2 x 3) : (3 x 2) = 6 : 6 = 1 : 1.

Q7. A invests Rs 25,000 and B invests Rs 35,000. If the total profit is Rs 12,000, find the share of A.
Answer: Rs 5,000
Solution: Ratio = 5 : 7. A = 12,000 x 5/12 = Rs 5,000.

Q8. Three partners invest 1/2, 1/3 and 1/6 of the total capital. If the profit is Rs 6,000, find the share of the largest investor.
Answer: Rs 3,000
Trick: Ratio = 1/2 : 1/3 : 1/6 = 3 : 2 : 1. Largest share = 6,000 x 3/6 = Rs 3,000.

Q9. A invests Rs 10,000 in a business. After 6 months, B joins with Rs 10,000. If the profit at the end of the year is Rs 9,000, find the share of B.
Answer: Rs 3,000
Solution: A = 10,000 x 12 and B = 10,000 x 6. Ratio = 2 : 1. B = 9,000 x 1/3 = Rs 3,000.

Q10. A and B invest in the ratio 3 : 5. If the total profit is Rs 4,000, find the share of A.
Answer: Rs 1,500
Solution: A = 4,000 x 3/8 = Rs 1,500.

Set 2: Joining Later, Salary and Mixed Partnership Questions (Q11–Q20)

Q11. A starts a business with Rs 20,000. After 4 months, B joins with Rs 30,000. If the profit at the end of the year is Rs 10,000, find the share of B.
Answer: Rs 5,000
Solution: A = 20,000 x 12 = 240,000 and B = 30,000 x 8 = 240,000. Ratio = 1 : 1. B = Rs 5,000.

Q12. A and B invest Rs 15,000 and Rs 20,000. A is a working partner and gets 10% of the profit as salary. If the total profit is Rs 7,000, find the total share of A.
Answer: Rs 3,400
Solution: Salary = Rs 700. Remaining = 6,300 divided in the ratio 3 : 4. A = 2,700 plus salary 700 = Rs 3,400.

Q13. The profits of A, B and C are in the ratio 2 : 3 : 5. If the share of A is Rs 4,000, find the total profit.
Answer: Rs 20,000
Solution: One part = 4,000 / 2 = 2,000. Total = 10 x 2,000 = Rs 20,000.

Q14. A, B and C invest Rs 5,000, Rs 7,000 and Rs 8,000 for 12, 10 and 6 months respectively. If the profit is Rs 8,900, find the share of B.
Answer: Rs 3,500
Solution: Ratio = 60,000 : 70,000 : 48,000 = 30 : 35 : 24. Sum = 89. B = 8,900 x 35/89 = Rs 3,500.

Q15. A invests Rs 4,000. After 3 months, B joins with Rs 6,000. If the profit at the end of the year is Rs 8,500, find the share of B.
Answer: Rs 4,500
Solution: A = 4,000 x 12 = 48,000 and B = 6,000 x 9 = 54,000. Ratio = 8 : 9. B = 8,500 x 9/17 = Rs 4,500.

Q16. The profits of A and B are in the ratio 3 : 5. B invested Rs 10,000 for the full year and A invested for 8 months. Find the capital of A.
Answer: Rs 9,000
Solution: A : B = (x x 8) : (10,000 x 12) = 3 : 5. So 40x = 360,000 and x = Rs 9,000.

Q17. A and B invest in the ratio 5 : 6. At the end of the year, B's profit is Rs 1,200 more than A's. Find the total profit.
Answer: Rs 13,200
Trick: Difference of 1 part = Rs 1,200. Total = 11 x 1,200 = Rs 13,200.

Q18. Four partners invest equal capital for 3, 4, 5 and 6 months. Find the ratio of their profits.
Answer: 3 : 4 : 5 : 6
Trick: With equal capital, the profit ratio equals the time ratio.

Q19. A, B and C invest Rs 5,000, Rs 8,000 and Rs 12,000. If the share of C in the profit is Rs 6,000, find the total profit.
Answer: Rs 12,500
Solution: Ratio = 5 : 8 : 12. C = 12/25 of the profit = 6,000. Total = 6,000 x 25/12 = Rs 12,500.

Q20. The profit of a business is Rs 15,000. A gets 1/3 of it, B gets 2/5 of the remaining and C gets the rest. Find the share of C.
Answer: Rs 6,000
Solution: A = 5,000. Remaining = 10,000. B = 4,000. C = 10,000 - 4,000 = Rs 6,000.

Set 3: Exam-Level Partnership Questions (Q21–Q30)

Q21. A and B invest Rs 8,000 and Rs 12,000. If the profit is Rs 6,000, find the difference between their shares.
Answer: Rs 1,200
Solution: Ratio = 2 : 3. A = 2,400 and B = 3,600. Difference = Rs 1,200.

Q22. The investments of A, B and C are in the ratio 2 : 3 : 4 for the same time. If the total profit is Rs 18,000, find the share of B.
Answer: Rs 6,000
Solution: B = 18,000 x 3/9 = Rs 6,000.

Q23. A and B invest Rs 1,000 and Rs 2,000 for the same time. The manager is paid 10% of the profit. If the total profit is Rs 10,000, find the share of A.
Answer: Rs 3,000
Solution: Manager = 1,000. Remaining = 9,000 divided in the ratio 1 : 2. A = Rs 3,000.

Q24. A and B invest Rs 70,000 and Rs 30,000. Out of a profit of Rs 20,000, find the share of A.
Answer: Rs 14,000
Solution: Ratio = 7 : 3. A = 20,000 x 7/10 = Rs 14,000.

Q25. What amount invested for 1 year gives the same profit as Rs 6,000 invested for 4 months?
Answer: Rs 2,000
Trick: 6,000 x 4 = 24,000 capital-months. For 12 months, capital = 24,000 / 12 = Rs 2,000.

Q26. A starts a business with Rs 50,000. B joins after 4 months. At the end of the year the profit is shared in the ratio 2 : 1 between A and B. Find the capital of B.
Answer: Rs 37,500
Solution: A = 50,000 x 12 = 600,000. B = x x 8. 600,000 : 8x = 2 : 1, so 8x = 300,000 and x = Rs 37,500.

Q27. Three partners invest in the ratio 3 : 4 : 5. The difference between the shares of the largest and the smallest partner is Rs 3,000. Find the total profit.
Answer: Rs 18,000
Solution: The difference of 2 parts = 3,000, so 1 part = 1,500. Total = 12 x 1,500 = Rs 18,000.

Q28. A and B invest Rs 20,000 and Rs 30,000. After 6 months, A adds Rs 10,000 more. If the profit at the end of the year is Rs 11,000, find the share of B.
Answer: Rs 6,000
Solution: A = 20,000 x 6 + 30,000 x 6 = 300,000. B = 30,000 x 12 = 360,000. Ratio = 5 : 6. B = 11,000 x 6/11 = Rs 6,000.

Q29. The total profit is Rs 24,000 and A, B and C share it in the ratio 1 : 2 : 3. Find the share of A.
Answer: Rs 4,000
Solution: A = 24,000 x 1/6 = Rs 4,000.

Q30. A, B and C invest in the ratio 1 : 2 : 3 for 3, 2 and 1 years respectively. If the profit is Rs 20,000, find the share of B.
Answer: Rs 8,000
Solution: Profit ratio = (1 x 3) : (2 x 2) : (3 x 1) = 3 : 4 : 3. B = 20,000 x 4/10 = Rs 8,000.

Common Mistakes in Partnership Questions

• Ignoring the time of investment and using only the capital ratio.
• Taking the wrong number of months for a partner who joins later.
• Forgetting to deduct the salary or commission before dividing the profit.
• Adding the capital instead of multiplying capital with time for changing capital.
• Not simplifying the ratio before dividing the profit.
• Making errors while converting fractions of capital into a ratio.

How to Practice These 30 Questions

1. Write the capital x time for every partner in a table.
2. Simplify the ratio first and then divide the profit.
3. Solve Set 1 in 6 minutes, Set 2 in 12 minutes and Set 3 in 12 minutes.
4. Use mental checks: the sum of all shares must equal the total profit.
5. Revise ratio and proportion before you attempt this paper.

Related Topics to Study Next

• Ratio and Proportion Questions
• Discount and Marked Price Questions
• Problems on Ages Questions
• SSC Previous Year Papers

Frequently Asked Questions

What is partnership in maths?

Partnership is a business in which two or more persons invest money and share the profit or loss according to their investment and the time for which the money stays in the business.

What is the formula for partnership?

Profit is shared in the ratio of (Capital x Time) of each partner. If the time is equal, the ratio of capital is used, and if the capital is equal, the ratio of time is used.

What is a sleeping partner?

A sleeping partner invests money but does not take part in the day-to-day management of the business. He gets profit only according to his investment.

How do I solve a question where a partner joins later?

Calculate the time of each partner in months (for example 12 months and 8 months), multiply with capital and then find the ratio.

How do I solve questions with a working partner?

First deduct the salary or commission of the working partner from the profit and then divide the remaining profit in the ratio of capital x time. Add his salary to his share.

What if the capital changes during the year?

Find capital x time for each period separately and add them for each partner, then find the ratio.

How many partnership questions come in SSC exams?

Usually one question per shift comes from partnership, and sometimes it is combined with ratio and profit and loss.

Are partnership questions related to ratio and proportion?

Yes. Partnership is an application of ratio and proportion, so a strong base in ratio makes partnership easy.

How do I solve a question when fractions of capital are given?

Convert the fractions into a ratio by taking the LCM of the denominators (for example, 1/2 : 1/3 : 1/6 = 3 : 2 : 1) and then divide the profit.

How should I prepare partnership for SSC exams?

Learn the capital x time rule, solve one set daily, practise different types (joining, leaving, salary) and then attempt previous year papers.