45+ Important CAT Partnership Questions with Answers [PDF Download] for Practice

Overview: Boost your CAT Quant score with 30+ CAT Partnership Questions to practice. Get exam-level problems with solutions, tips, and tricks to master this high-scoring Arithmetic topic. Read on to know more!

Partnership questions in CAT are a part of the Arithmetic section and are generally simple if your basics are clear.

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These questions are based on real-life business scenarios where two or more people invest money and share profits or losses.

The trick lies in understanding how capital and time affect the profit-sharing ratio. With the right approach and practice, you can solve most partnership questions in under a minute, making them a great opportunity to score easy marks in the CAT exam!

Continue reading to learn about the different types of partnership CAT questions here!

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What are CAT Partnership Questions?

Partnership questions test your understanding of profit-sharing in business or investment situations. These problems typically revolve around:

• Capital contribution
• Time of investment
• Profit-sharing ratio
• Working and sleeping partners

In the CAT Quantitative Aptitude section, Partnership questions often appear under Arithmetic and are usually considered easy to moderate in difficulty, perfect for scoring quick marks!

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Mid Level CAT Partnership Questions 2025 to Practice

1. A and B invest ₹20,000 and ₹25,000 respectively in a business. After 4 months, A withdraws ₹5,000 and B adds ₹5,000. At the end of a year, what is the ratio of their profits?

A) 1:1
B) 16:25
C) 19:26
D) 21:29
✅ Answer: D) 21:29

2. A started a business with ₹50,000. After 6 months, B joined with ₹30,000. At the end of the year, what is the profit-sharing ratio?

A) 5:3
B) 2:1
C) 10:3
D) 5:2
✅ Answer: A) 5:3

3. A, B, and C invest in the ratio 2:3:5. The time period of investment is 6 months, 4 months, and 3 months, respectively. What is the ratio of their profits?

A) 2:3:5
B) 1:1:1
C) 1:1:2
D) 1:1:1.5
✅ Answer: C) 1:1:2

4. A and B invest ₹60,000 and ₹90,000 respectively. After 5 months, B withdraws ₹30,000. What is the ratio of their profits after 10 months?

A) 1:1
B) 3:4
C) 5:6
D) 6:7
✅ Answer: C) 5:6

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5. A invests ₹1,00,000. B joins after 3 months with ₹80,000. The total profit at the end of the year is ₹96,000. What is B’s share?

A) ₹32,000
B) ₹24,000
C) ₹28,000
D) ₹36,000
✅ Answer: B) ₹24,000

6. A invests ₹5000 more than B. If their investment durations are equal and A’s profit is ₹1800 and B’s is ₹1200, find B’s capital.

A) ₹7,000
B) ₹8,000
C) ₹6,000
D) ₹5,000
✅ Answer: C) ₹6,000

7. In a business, A and B are partners in the ratio 3:2. A gets ₹600 more than B. What is the total profit?

A) ₹3,000
B) ₹2,400
C) ₹2,000
D) ₹1,800
✅ Answer: A) ₹3,000

8. A invests ₹40,000 and B invests ₹50,000. After 3 months, A adds ₹10,000 more and B withdraws ₹10,000. Find the profit ratio after 6 months.

A) 1:1
B) 5:4
C) 4:3
D) 7:6
✅ Answer: D) 7:6

9. A, B, and C start a business with investments in the ratio 4:5:6. If the profit at year-end is ₹78,000, find B’s share.

A) ₹26,000
B) ₹30,000
C) ₹28,000
D) ₹24,000
✅ Answer: A) ₹26,000

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10. A and B share profits in 7:5. If A’s capital was ₹70,000 for 12 months, what was B’s investment for the same period?

A) ₹50,000
B) ₹60,000
C) ₹40,000
D) ₹30,000
✅ Answer: A) ₹50,000

11. A, B, and C invest ₹6000, ₹8000, and ₹10,000 respectively. After 1 year, the profit is ₹9,000. Find C’s share.

A) ₹3,000
B) ₹4,000
C) ₹3,600
D) ₹3,200
✅ Answer: A) ₹3,000

12. A starts a business, and after 3 months, B joins with 75% of A's capital. At year-end, B’s share of profit is ₹9000. What is A’s profit?

A) ₹12,000
B) ₹10,000
C) ₹9,000
D) ₹11,000
✅ Answer: A) ₹12,000

13. A invests ₹10000 and B ₹15000. After 4 months, A adds ₹5000 and B withdraws ₹5000. What is the profit ratio after a year?

A) 13:17
B) 15:18
C) 11:14
D) 14:15
✅ Answer: A) 13:17

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14. A and B invested ₹40000 and ₹50000. After 5 months, A left, and B continued for 7 more months. What is the ratio of their profits?

A) 2:5
B) 1:2
C) 4:5
D) 3:4
✅ Answer: C) 4:5

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15. A and B start a business with investments in the ratio 5:6. A receives ₹1500 more than B. Find the total profit.

A) ₹16,500
B) ₹18,000
C) ₹19,500
D) ₹20,000
✅ Answer: B) ₹18,000

16. A and B share profits in the ratio 2:3. If A invests for 8 months and B for 6 months, find their investment ratio.

A) 4:3
B) 2:1
C) 3:2
D) 3:4
✅ Answer: A) 4:3

17. A, B, and C invested ₹50,000, ₹60,000, and ₹90,000, respectively for 6 months. Find A’s share in ₹40,000 profit.

A) ₹8,000
B) ₹9,000
C) ₹10,000
D) ₹7,500
✅ Answer: A) ₹8,000

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18. A started a business and was joined by B after 4 months. If A invested ₹60,000 and B ₹90,000, find their profit ratio after a year.

A) 2:3
B) 3:4
C) 3:5
D) 4:5
✅ Answer: C) 3:5

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19. A, B, and C are partners in a business. A gets 2/5 of the profit, and B gets 1/4 of the profit. If C’s share is ₹7,500, find the total profit.

A) ₹25,000
B) ₹30,000
C) ₹20,000
D) ₹24,000
✅ Answer: A) ₹25,000

20. A, B, and C invest ₹10000, ₹15000, and ₹20000, respectively, for a year. C is also a working partner and gets ₹2000 extra. Total profit is ₹13,000. Find C’s total share.

A) ₹5,000
B) ₹6,000
C) ₹7,000
D) ₹8,000
✅ Answer: C) ₹7,000

21. A and B invest ₹50,000 and ₹70,000 respectively. After 4 months, A adds ₹20,000. What is the ratio of profit at year-end?

A) 37:49
B) 35:52
C) 38:53
D) 39:51
✅ Answer: A) 37:49

22. A starts a business with ₹1,00,000. B joins after 6 months with ₹1,50,000. If total profit is ₹90,000, what is A’s share?

A) ₹40,000
B) ₹45,000
C) ₹50,000
D) ₹60,000
✅ Answer: D) ₹60,000

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23. A, B, and C invest ₹60000, ₹80000, and ₹1,00,000. After 6 months, they withdrew half of their investments. Find the profit share ratio after a year.

A) 6:8:10
B) 1:1:1
C) 3:4:5
D) 9:12:15
✅ Answer: D) 9:12:15

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24. A receives 2/3 of the profit and B the rest. If B’s profit is ₹4000, what is the total profit?

A) ₹8,000
B) ₹12,000
C) ₹10,000
D) ₹6,000
✅ Answer: C) ₹10,000

25. A invested ₹15,000 for 12 months, B ₹10,000 for 6 months, and C ₹12,000 for 4 months. Who gets the highest profit?

A) A
B) B
C) C
D) All equal
✅ Answer: A) A

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High-Level CAT Partnership Questions 2025 to Practice

26. A started a business with ₹60,000. After 3 months, B joined with ₹75,000. After 2 more months, C joined with ₹90,000. At the end of the year, the total profit was ₹1,48,000. Find C’s share.

A) ₹28,000
B) ₹30,000
C) ₹32,000
D) ₹34,000
✅ Answer: C) ₹32,000

27. A and B start a business with capital in the ratio 3:2. After 4 months, C joins with capital equal to B. At the end of the year, the profit is ₹1,20,000. If C’s share is ₹20,000, find A’s share.

A) ₹50,000
B) ₹60,000
C) ₹65,000
D) ₹70,000
✅ Answer: B) ₹60,000

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28. A, B, and C start a business. A invests ₹80,000 for the full year. B invests ₹1,20,000 for 8 months, and C invests ₹1,60,000 for 6 months. If C gets ₹24,000 as profit, what is the total profit?

A) ₹60,000
B) ₹54,000
C) ₹72,000
D) ₹80,000
✅ Answer: C) ₹72,000

29. A is a working partner, and B is a sleeping partner. A invests ₹60,000 and B ₹90,000. A gets 10% of the profit as salary, and the remaining is shared in the ratio of their investments. If A gets a total of ₹36,000, find the total profit.

A) ₹80,000
B) ₹90,000
C) ₹1,00,000
D) ₹1,20,000
✅ Answer: B) ₹90,000

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30. A and B invested ₹40,000 and ₹60,000 respectively. After 6 months, they reinvested profits in a ratio equal to their initial profit shares. If at the end of 1 year, total profit was ₹66,000, what was B’s final share?

A) ₹38,000
B) ₹40,000
C) ₹42,000
D) ₹44,000
✅ Answer: C) ₹42,000

31. A, B, and C started a partnership. A and B invested ₹50,000 and ₹75,000 respectively. After 6 months, C joins with ₹1,00,000. At the end of the year, the profit is divided equally. What amount did C lose or gain compared to his deserved share?

A) Gained ₹2,500
B) Lost ₹5,000
C) Gained ₹5,000
D) Lost ₹2,500
✅ Answer: B) Lost ₹5,000

32. A, B, and C enter a business. A invests ₹1,20,000. B joins after 2 months with ₹1,50,000, and C joins after 4 months with ₹1,80,000. If the profit at the end of the year is ₹1,02,000, what is B’s share?

A) ₹34,000
B) ₹30,000
C) ₹32,000
D) ₹36,000
✅ Answer: A) ₹34,000

33. A, B, and C start a business. A invests ₹1,00,000, B invests ₹80,000, and C invests ₹60,000 for 12, 9, and 6 months, respectively. If C receives ₹8,000 as his share, how much more should A have received compared to C?

A) ₹8,000
B) ₹12,000
C) ₹14,000
D) ₹16,000
✅ Answer: D) ₹16,000

34. A starts a business with ₹60,000. B joins after 4 months with ₹90,000. After 3 more months, C joins with ₹1,20,000. If total profit is ₹1,48,500, find A's share.

A) ₹43,000
B) ₹44,000
C) ₹45,000
D) ₹46,000
✅ Answer: C) ₹45,000

35. A and B start a business with ₹1,20,000 and ₹80,000 respectively. After 5 months, B adds ₹40,000 more and A withdraws ₹20,000. What is their profit ratio at the end of the year?

A) 4:3
B) 3:2
C) 37:29
D) 39:31
✅ Answer: C) 37:29

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Advanced CAT Partnership Questions 2025 for Practice

36. A started a business with ₹90,000. After 3 months, B joined with ₹1,20,000. After another 3 months, C joined with ₹1,50,000. If the total profit at the end of the year is ₹2,40,000, what is A’s share?

A) ₹90,000
B) ₹84,000
C) ₹72,000
D) ₹78,000
✅ Answer: B) ₹84,000

37. A and B start a business with ₹1,00,000 and ₹50,000 respectively. After 6 months, A takes out ₹25,000 and B adds ₹25,000. What is the profit-sharing ratio after a year?

A) 3:2
B) 7:5
C) 5:3
D) 13:9
✅ Answer: D) 13:9

38. A, B, and C invested ₹60,000, ₹1,20,000, and ₹90,000, respectively. A remained in the business for 12 months, B for 8 months, and C for 6 months. If total profit is ₹1,26,000, what is C’s share?

A) ₹24,000
B) ₹28,000
C) ₹30,000
D) ₹32,000
✅ Answer: C) ₹30,000

39. A and B start a business. A invests ₹70,000 for 6 months. B joins later and invests ₹1,05,000 for 4 months. If A’s profit share is ₹9,000, what is the total profit?

A) ₹15,000
B) ₹16,000
C) ₹17,000
D) ₹18,000
✅ Answer: A) ₹15,000

40. A and B are partners. A receives 10% of the profit as salary and the remaining is divided in the ratio 3:2. If A gets ₹8,400 out of total ₹12,000 profit, find B’s share.

A) ₹3,600
B) ₹3,400
C) ₹3,200
D) ₹3,000
✅ Answer: B) ₹3,400

41. A invested ₹80,000 for the full year. B joined after 3 months with ₹60,000. After another 3 months, C joins with ₹40,000. If total profit is ₹74,000, find C’s share.

A) ₹8,000
B) ₹10,000
C) ₹12,000
D) ₹14,000
✅ Answer: A) ₹8,000

42. A, B, and C started a business with investments in the ratio 5:6:7. After 4 months, A withdrew half of his capital, B doubled his capital, and C increased his investment by 50%. What is the new profit-sharing ratio at the end of the year?

A) 23:35:37
B) 21:36:41
C) 25:38:42
D) 22:34:39
✅ Answer: B) 21:36:41

43. A and B start a business. A invests ₹1,00,000 and B ₹50,000. After 4 months, A withdraws ₹25,000 and B adds ₹25,000. After 8 months, both withdraw ₹25,000 each. What is the profit-sharing ratio at year-end?

A) 19:11
B) 17:13
C) 18:12
D) 20:15
✅ Answer: A) 19:11

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44. A and B start a business with ₹80,000 and ₹1,20,000. After 6 months, C joins with ₹2,00,000. A and B leave the business after 9 months. What is the ratio of A, B, and C's profit at the end of the year?

A) 6:9:10
B) 4:6:7
C) 6:9:8
D) 3:4:8
✅ Answer: C) 6:9:8

45. A and B are in a partnership. A receives 20% of the profit for managing the business, and the rest is divided in the ratio of their capitals, 4:3. If A gets ₹4,400 more than B, what is the total profit?

A) ₹24,000
B) ₹28,000
C) ₹30,000
D) ₹32,000
✅ Answer: C) ₹30,000

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Key Concepts in CAT Partnership Questions 2025

The core idea behind these questions is the relationship between capital, time, and profit. The profit or loss in a partnership is generally distributed among the partners in proportion to their investments and the time for which the investments were made.

The key formula used in partnership questions is:

Profit Ratio = (Capital 1 × Time 1) : (Capital 2 × Time 2) : (Capital 3 × Time 3): ...

Where:

• Capital: The amount of money invested by a partner.
• Time: The duration for which the capital is invested.
• Profit: The share of profit or loss for each partner.

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Types of CAT Partnership Questions 2025

There are two main types of partnership questions you can expect in the CAT exam:

1. Simple Partnership:

In this type, all partners invest their capital for the same duration. The profit is distributed in proportion to their investments.

Example: A and B start a business with investments of Rs. 20,000 and Rs. 30,000, respectively. If the total profit is Rs. 15,000, what is the profit-sharing ratio?

• Since the time period is the same, the profit-sharing ratio is simply the ratio of their investments: A: B = 20,000 : 30,000 = 2:3.
• Then, the total profit of Rs. 15,000 is distributed in this ratio.

2. Compound Partnership:

In this type, different partners invest their money for different time periods. In this case, the profit-sharing ratio is calculated by multiplying each partner's capital by the time period for which it was invested.

Example: A invests Rs. 40,000 for 9 months, and B invests Rs. 60,000 for 6 months. If the total profit is Rs. 24,000, what is B's share?

• Ratio of their effective investments (Capital × Time): A:B = (40,000 × 9) : (60,000 × 6) = 360,000 : 360,000 = 1:1.
• So, the profit is shared equally. B's share would be Rs. 12,000.

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CAT Partnership Questions: Common Variations and Scenarios

CAT partnership questions can have various twists and scenarios, such as:

• Changes in Investment: A partner might increase or decrease their investment after a certain period.
• New Partner Joining: A new partner might join the business after a few months with their own investment.
• Working Partner: One partner may be a "working partner" who receives a certain percentage of the profit for managing the business, while the remaining profit is distributed among all partners based on their individual investments.
• Profit Sharing Ratio is Given: Instead of asking for the profit share, the question might provide the profit ratio and ask for the time period or investment of a partner.

Rent/Expense Sharing: These problems can also involve sharing rent or other expenses based on the usage of a resource.