Partnership – MBA CUET PG – Notes & Practice Questions

Definition

A partnership is a business arrangement where two or more individuals invest money and share profit in proportion to their contributions.

Profit distribution depends on:

• Amount of capital invested
• Duration of investment

Types of Partnership

A. Simple Partnership:

All partners invest for the same duration.
Profit is shared in the ratio of investments.

Formula:
Profit share ∝ Capital invested

B. Compound (Time-based) Partnership:

Partners invest for different periods of time.
Profit is shared in the ratio of Capital × Time.

Formula:
Profit Ratio = (C₁ × T₁) : (C₂ × T₂) : (C₃ × T₃) …

Key Formulas

Profit Sharing Ratio:

$$\text{Profit Ratio}=(\text{Investment}\times \text{Time})$$

If partner joins late or withdraws early

Adjust time accordingly.

Example:
A invests for 12 months, B invests for 8 months →
Ratio = (C₁ × 12) : (C₂ × 8)

To find Capital when Profit and Time are given

$$C_A : C_B = \frac{P_A}{T_A} : \frac{P_B}{T_B}$$

Important Concepts

Active Partner:

Participates in business + invests capital.

Sleeping Partner:

Only invests capital, does not participate in operations.

Salary / Commission to a Partner:

If a partner receives salary/commission:

1. Deduct salary/commission from total profit

2. Remaining profit shared in investment × time ratio

Standard Cases

Case 1: Same Time, Different Capitals

$$\text{Profit Ratio} = C_A : C_B : C_C$$

Case 2: Different Time and Capital

$$\text{Profit Ratio}=(C_A\times T_A):(C_B\times T_B)$$

Case 3: Partner Joins Later

Adjust time for each partner according to actual participation.

Case 4: Partner Withdraws Capital Early

Use the period for which the capital was active.

Case 5: Multiple Changes in Capital

If a partner changes capital midway:
Calculate contribution for each period separately.

Example:
A invests 10,000 for 6 months, then 15,000 for next 6 months →
Total = (10,000 × 6) + (15,000 × 6)

Solved Examples

Example 1: Simple Partnership

A invests 40,000 and B invests 60,000 for the same time.
Profit = 50,000

Ratio = 40,000 : 60,000 = 2 : 3
A’s share = (2/5) × 50,000 = 20,000
B’s share = (3/5) × 50,000 = 30,000

Example 2: Time-Based Partnership

A invests 50,000 for 12 months
B invests 60,000 for 9 months

Profit Ratio = (50,000 × 12) : (60,000 × 9)
= 600,000 : 540,000 = 10 : 9

Example 3: Salary + Profit

A and B invest equally.
A gets a salary of 1,000 per month.
Total profit = 90,000
Duration = 12 months

A’s salary = 1,000 × 12 = 12,000
Remaining profit = 90,000 – 12,000 = 78,000

Since capital is equal:
A’s share = 78,000 / 2 = 39,000
B’s share = 39,000

Final share:
A = 39,000 + 12,000 = 51,000
B = 39,000

Example 4: Partner Joins Later

A invests 80,000 for 1 year
B joins after 3 months with 1,20,000

Time of B = 9 months

Profit Ratio = (80,000 × 12) : (1,20,000 × 9)
= 960,000 : 1,080,000
= 8 : 9

Shortcut

• Profit ∝ Capital × Time

• For partners joining later → reduce time

• For partners withdrawing early → reduce time

• Salary or commission is always deducted before division

• When capital changes midway → break into segments

Practice Questions

1. A invests ₹80,000 for 12 months, B invests ₹1,20,000 for 9 months, C invests ₹60,000 for 6 months. If total profit = ₹1,80,000, what is C’s share?

A) ₹18,000
B) ₹20,000
C) ₹24,000
D) ₹30,000

2. A and B invest in ratio 5:3 and withdraw half capital after 4 months. Profit at year end = ₹96,000. What is B’s share?

A) ₹24,800
B) ₹26,800
C) ₹28,800
D) ₹30,800

3. A, B, C invest in ratio 2:3:4. After 6 months, A doubles money, B withdraws 1/3 capital, C withdraws completely. Profit ratio?

A) 20:27:24
B) 27:20:24
C) 24:20:27
D) 27:24:20

4. A invests ₹90,000; after 3 months B joins with ₹1,20,000; after 3 more months C joins with ₹1,50,000. Total profit = ₹2,40,000. A’s share?

A) ₹68,000
B) ₹70,000
C) ₹72,000
D) ₹80,000

5. A invests ₹60,000. After 5 months B joins with ₹90,000. B receives ₹15,000 more than A. What is total profit?

A) ₹70,000
B) ₹75,000
C) ₹80,000
D) ₹85,000

6. A & B invest ₹40,000 & ₹60,000. After 4 months A adds ₹40,000. Profit = ₹1,50,000. A’s share?

A) ₹84,000
B) ₹90,000
C) ₹96,000
D) ₹100,000

7. A invests ₹80,000 for 12 months; B invests ₹70,000 for 9 months; C invests ₹60,000 for 7 months. A’s profit = ₹24,000. What is total profit?

A) ₹70,000
B) ₹72,000
C) ₹75,000
D) ₹80,000

8. A & B invest in ratio 3:5. After 6 months A increases capital by 50% & B decreases by 20%. Profit ratio?

A) 21:35
B) 20:35
C) 25:35
D) 21:30

9. A, B, C invest in ratio 4:6:9. Investment period ratio is 3:4:6. If C gets ₹27,000, total profit?

A) ₹60,000
B) ₹66,000
C) ₹72,000
D) ₹75,000

10. A invests ₹1,00,000 for 8 months, B invests ₹80,000 for 10 months. B gets ₹4,000 more. Total profit?

A) ₹32,000
B) ₹34,000
C) ₹36,000
D) ₹40,000

11. A invests ₹1,20,000; B invests ₹2,00,000. B gets ₹15,000 more. C (active partner) received ₹12,000 salary. Remaining shared in ratio. Find total profit.

A) ₹1,10,000
B) ₹1,13,000
C) ₹1,17,000
D) ₹1,20,000

12. A invests for 6 months; B for 8 months. A:B profit = 9:16. A invests ₹54,000. B’s investment?

A) ₹60,000
B) ₹64,000
C) ₹72,000
D) ₹80,000

13. A invests 12 months; B joins after 3 months; C after 6 months investing 70k, 80k, & 90k. Profit ratio?

A) 28:32:27
B) 30:32:27
C) 28:30:27
D) 20:30:27

14. A invests ₹2,40,000; B joins after 5 months with ₹3,00,000; C joins after 9 months with ₹3,60,000. Total profit ₹3,36,000. B’s share?

A) ₹92,000
B) ₹95,000
C) ₹1,00,000
D) ₹1,08,000

15. A,B,C invest 50k, 60k, 90k. B invests 10 months, C 8 months. A’s share = ₹40,000. B’s share?

A) ₹45,000
B) ₹46,000
C) ₹47,000
D) ₹48,000

16. Profit ratio A:B = 7:9. A invests 6 months, B 8 months. B invests ₹36,000. A’s capital?

A) ₹26,000
B) ₹27,000
C) ₹28,000
D) ₹30,000

17. A invests 25%, B 35%, C the rest. Time = 12, 8, 6 months. Profit ratio?

A) 18:14:9
B) 14:18:9
C) 18:9:14
D) 12:14:9

18. A & B invest equal money. A gets salary ₹12,000. Remaining profit divided 3:5. Total profit = ₹1,04,000. B’s share?

A) ₹46,000
B) ₹48,000
C) ₹50,000
D) ₹52,000

19. A invests 80k; B invests 50k. A gets ₹2,000/month salary. Total profit = 1,44,000. B’s share?

A) ₹39,000
B) ₹40,000
C) ₹42,000
D) ₹45,000

20. A invests 70k; B 90k; C joins after 4 months with 1,20,000. Profit ratio?

A) 7:9:8
B) 9:7:8
C) 7:8:9
D) 9:8:7

21. A invests 1,50,000 for 6 months; B invests 1,00,000 for 12 months. B gets 20k more. Total profit?

A) 1,00,000
B) 1,05,000
C) 1,08,000
D) 1,12,000

22. A & B invest 40k and 50k. A works and gets salary 10% of total profit. Remaining shared 4:5. A’s total share = 36,000. Find total profit.

A) 75,000
B) 80,000
C) 90,000
D) 1,00,000

23. A invests 75k for whole year; B invests 45k for 8 months; C invests unknown for 6 months. Profit ratio A:B:C = 5:3:2. C’s investment?

A) 24k
B) 30k
C) 36k
D) 40k

24. A & B invest 2:3. After 6 months A withdraws half; B adds 1/3. Profit ratio?

A) 3:5
B) 4:7
C) 5:8
D) 6:11

25. A invests 1,20,000; B invests 90,000; C invests 60,000. Times are 12, 8, 6 months. Profit = 2,34,000. B’s share?

A) 60,000
B) 62,000
C) 64,000
D) 66,000

26. A invests for 4 months & B for 8 months. Profit ratio 1:2. If B invested 80k, A invested?

A) 40k
B) 30k
C) 20k
D) 50k

27. A starts with 50k, B after 3 months with 40k, C after 6 months with 30k. Profit = 1,20,000. C’s share?

A) 20k
B) 22,500
C) 25k
D) 30k

28. A & B invest 80k & 20k. B works and gets salary 12,000. Total profit = 1,00,000. A’s share?

A) 64k
B) 68k
C) 70k
D) 72k

29. A invests 90k; B 1,10,000; C 1,50,000. Times 10, 8, 6 months. Ratio?

A) 45:44:50
B) 45:40:50
C) 50:45:44
D) 44:45:50

30. A & B invest 3:4. Profit ratio = 2:5. If A invested for 10 months, B invested for?

A) 20
B) 25
C) 12
D) 15

31. A invests 50k. B invests x for 8 months. Profit ratio 5:8. x?

A) 60k
B) 70k
C) 80k
D) 90k

32. A invests 2/5 of total, B invests 1/3, C rest. Time = 12, 10, 8 months. Profit = 4,80,000. C’s share?

A) 1,20,000
B) 1,30,000
C) 1,40,000
D) 1,44,000

33. A invests 30k; B invests 45k; C invests 60k. A withdraws after 6 months; others remain 12 months. Ratio?

A) 1:2:4
B) 1:3:4
C) 1:3:6
D) 1:4:5

34. A invests 5 months; B invests 8 months. B’s capital = 40k. Profit ratio = 1:2. A’s capital?

A) 30k
B) 25k
C) 20k
D) 18k

35. A invests 60k; B joins after 2 months with 50k; C joins after 4 months with 40k. Profit = 96,000. B’s share?

A) 25k
B) 24k
C) 22k
D) 20k

36. A invests x for 8 months & B invests 60k for 12 months. Profit ratio = 2:3. Find x.

A) 30k
B) 32k
C) 40k
D) 45k

37. A invests 100k, B invests 120k, C invests 150k. Times = 12, 10, 8 months. C gets 45,000. Total profit?

A) 90k
B) 1,00k
C) 1,20k
D) 1,35k

38. A invests 2x for 6 months; B invests 3x for 4 months; C invests x for 12 months. Ratio?

A) 3:2:2
B) 2:3:2
C) 2:2:3
D) 1:2:3

39. A invests 90k for 12 months; B invests 120k for 6 months; C invests 110k for 4 months. Profit = 1,80,000. C’s share?

A) 30k
B) 32k
C) 36k
D) 40k

40. A & B invest equal. A gets 20% of profit as salary. Remaining shared equally. A total share = 36,000. Total profit?

A) 50k
B) 55k
C) 60k
D) 62k

41. A invests 40k for 12 months; B invests 60k for x months. Profit ratio = 4:3. Find x.

A) 6
B) 8
C) 9
D) 10

42. A invests 90k for 10 months; B 80k for 12 months. Profit = 72k. A’s share?

A) 30k
B) 32k
C) 34k
D) 36k

43. A invests 60k; B invests 80k; C works gets 20% profit. Remaining shared equally. Total profit 1,20,000. B’s share?

A) 30k
B) 32k
C) 36k
D) 40k

44. A invests x for 5 months; B invests 50k for 8 months. Profit ratio = 1:2. x?

A) 15k
B) 20k
C) 25k
D) 30k

45. A invests 75k; B invests 90k. B gets 20% more profit. Time equal. Total profit?

A) 1,30k
B) 1,35k
C) 1,40k
D) 1,45k

46. A invests 45k for 9 months; B invests 60k for 6 months; C invests 75k for 3 months. Ratio?

A) 27:20:15
B) 27:30:15
C) 27:20:12
D) 27:25:15

47. A invests 120k; B invests 80k; C invests 1/3 more than B. Time equal. Ratio?

A) 9:6:8
B) 6:9:8
C) 8:9:6
D) 9:8:6

48. A invests 3x; B invests 2x; C invests x. Time equal. A gets 36k. Total profit?

A) 60k
B) 72k
C) 80k
D) 90k

49. A invests 80k; B invests 1,00k; C joins after 3 months with 60k. Profit = 1,20k. C’s share?

A) 15k
B) 16k
C) 18k
D) 20k

50. A invests 40k for 12 months; B invests 24k for 15 months. Ratio?

A) 4:3
B) 5:4
C) 6:5
D) 10:9

51. A invests 2/3 capital for 8 months; B invests rest for 12 months. Profit ratio A:B?

A) 2:3
B) 4:3
C) 3:2
D) 8:9

52. A invests 60k; B invests 70k; C invests 80k. C withdraws after 6 months; A & B stay 12 months. Ratio?

A) 12:14:6
B) 12:14:8
C) 12:14:10
D) 12:14:12

53. A invests 100k for 12 months; B invests x for 9 months; Profit ratio = 4:3. x?

A) 70k
B) 75k
C) 80k
D) 85k

54. A invests 60k; B invests 90k; C invests 120k. Times 8, 6, 4 months. Ratio?

A) 480:540:480
B) 480:540:600
C) 480:560:600
D) 480:600:540

55. A invests 80k for 12 months; B invests 60k for 15 months. Profit = 1,20k. A’s share?

A) 50k
B) 52k
C) 56k
D) 60k

56. A invests 40k; B invests 50k. A withdraws at 8 months; B stays 12 months. Profit = 54k. A’s share?

A) 18k
B) 20k
C) 22k
D) 24k

57. A invests 1/4 of total; B invests 1/3; C rest. Time = 10, 8, 12. Ratio?

A) 10:8:?(calc)
Options:
A) 10:8:9
B) 15:12:10
C) 10:8:12
D) 10:8:6

58. A invests 90k; B invests 70k; C invests 50k. A withdraws at 9 months; B at 6 months; C full year. Ratio?

A) 810:420:600
B) 810:480:600
C) 810:420:500
D) 900:480:600

59. A invests x; B invests 60k. Time equal. Profit ratio 3:4. x?

A) 40k
B) 45k
C) 48k
D) 52k

60. A invests 120k for 6 months; B invests 80k for 12 months; C invests 100k for 8 months. Profit = 2,40k. C’s share?

A) 60k
B) 64k
C) 70k
D) 72k

61. A invests 3/5 capital for 12 months; B invests rest for 8 months. Ratio?

A) 36:16
B) 45:32
C) 36:22
D) 30:16

62. A invests 60k whole year; B invests 50k for 6 months; C invests 40k for 3 months. Ratio?

A) 60:25:10
B) 60:30:20
C) 60:40:25
D) 60:20:10

63. A invests 1,00,000; B invests x for 6 months; Profit ratio 5:3. x?

A) 72k
B) 75k
C) 80k
D) 85k

64. A invests 2/3 of capital for 6 months; B invests rest for 12 months. Ratio?

A) 2:3
B) 4:3
C) 1:1
D) 8:9

65. A invests 90k for 12 months; B invests 120k for 8 months; C invests 150k for 4 months. Profit = 1,80k. A’s share?

A) 72k
B) 75k
C) 78k
D) 80k

66. A invests x; B invests 40k; C invests 60k. Profit ratio = 3:4:6. x?

A) 45k
B) 48k
C) 50k
D) 52k

67. A invests 50k for 6 months; B invests 60k for 4 months; C invests unknown for 8 months. Ratio A:B:C = 15:12:16. C invests?

A) 40k
B) 48k
C) 50k
D) 60k

68. A invests 80k for 5 months; B invests 100k for x months. Profit ratio 4:5. x?

A) 5
B) 6
C) 7
D) 8

69. A invests 75k full year; B invests 60k for 6 months; C invests 90k for 3 months. Profit = 1,26k. B’s share?

A) 15k
B) 18k
C) 20k
D) 22k

70. A invests 1,20,000 for 12 months; B invests x for 8 months; C invests 60,000 for 6 months. Ratio A:B:C = 24:16:9. x?

A) 80k
B) 85k
C) 90k
D) 95k