Question 1

A and B enter into a partnership. A invests ₹4,500 and B invests ₹5,500. After one year, the profit is ₹2,000. What is A's share of the profit?

Accepted Answer

Step 1: In a partnership, profit is divided in the ratio of investments. Step 2: Ratio of A's investment to B's investment = 4,500 : 5,500 = 9 : 11. Step 3: Total parts = 9 + 11 = 20. Step 4: A's share = (9/20) × 2,000 = ₹900.

Question 2

Three partners invest ₹12,000, ₹15,000, and ₹18,000 respectively. The profit earned is ₹9,000. What is the difference between the highest and lowest profit shares?

Accepted Answer

Step 1: Investment ratio = 12,000 : 15,000 : 18,000 = 4 : 5 : 6 (divide by 3,000). Step 2: Total parts = 4 + 5 + 6 = 15. Step 3: Lowest profit share = (4/15) × 9,000 = ₹2,400. Step 4: Highest profit share = (6/15) × 9,000 = ₹3,600. Step 5: Difference = 3,600 - 2,400 = ₹1,200.

Question 3

A, B, and C invest ₹6,000, ₹8,000, and ₹10,000 respectively. They agree to share profits in the ratio of their investments. If C's profit is ₹2,500, what is the total profit?

Accepted Answer

Step 1: Investment ratio A : B : C = 6,000 : 8,000 : 10,000 = 3 : 4 : 5. Step 2: Total parts = 3 + 4 + 5 = 12. Step 3: C's share is 5 parts out of 12. Step 4: If C's profit = ₹2,500, then (5/12) × Total Profit = 2,500. Step 5: Total Profit = 2,500 × (12/5) = ₹6,000.

Question 4

X, Y, and Z start a business with investments in the ratio 2 : 3 : 4. If the total profit at the end of the year is ₹1,800, what is Z's share?

Accepted Answer

Step 1: Investment ratio = 2 : 3 : 4. Step 2: Total parts = 2 + 3 + 4 = 9. Step 3: Z's share = (4/9) × 1,800 = ₹800.

Question 5

A and B are partners in a business. A's capital is ₹50,000 and B's capital is ₹40,000. They agree to share profits in the ratio 5:3. If A withdraws ₹10,000 after 4 months, what is the ratio of their capital contributions for the year (considering the withdrawal)?

Accepted Answer

Step 1: A's capital for 4 months = ₹50,000. A's capital for remaining 8 months = ₹50,000 - ₹10,000 = ₹40,000. Step 2: A's capital-time = (50,000 × 4) + (40,000 × 8) = 200,000 + 320,000 = 520,000. Step 3: B's capital-time = 40,000 × 12 = 480,000. Step 4: Ratio of capital contributions = 520,000:480,000 = 13:12 (divide by 40,000).

Question 6

Two partners, M and N, invest in a business in the ratio 5 : 7. If M's profit is ₹1,500, what is N's profit?

Accepted Answer

Step 1: Investment ratio M : N = 5 : 7. Step 2: Profit is distributed in the same ratio. Step 3: If M's profit = ₹1,500 and M's ratio part = 5, then 1 ratio part = 1,500/5 = ₹300. Step 4: N's profit = 7 × 300 = ₹2,100.

Question 7

A and B enter into a partnership. A invests ₹12,000 for 8 months and B invests ₹15,000 for 6 months. If the total profit is ₹4,620, what is A's share of the profit?

Accepted Answer

Step 1: Calculate capital × time for each partner. A's contribution = 12,000 × 8 = 96,000. B's contribution = 15,000 × 6 = 90,000. Step 2: Find the ratio of contributions: A:B = 96,000:90,000 = 16:15. Step 3: Divide profit in the ratio 16:15. Total parts = 16 + 15 = 31. A's share = (16/31) × 4,620 = ₹2,400.

Question 8

P, Q, and R start a business with investments in the ratio 3:4:5. If the total profit after one year is ₹3,600, what is R's profit share?

Accepted Answer

Step 1: The investments are in ratio P:Q:R = 3:4:5. Step 2: Since all invest for the same time period (1 year), profit is distributed in the same ratio as investment. Step 3: Total parts = 3 + 4 + 5 = 12. Step 4: R's share = (5/12) × 3,600 = 5 × 300 = ₹1,500.

Question 9

X and Y form a partnership. X contributes ₹20,000 and Y contributes ₹30,000. After 6 months, Z joins with ₹25,000. If the profit at the end of the year is ₹9,000, how much profit does Z receive?

Accepted Answer

Step 1: Calculate capital × time for each partner. X's contribution = 20,000 × 12 = 240,000. Y's contribution = 30,000 × 12 = 360,000. Z's contribution = 25,000 × 6 = 150,000 (Z joined after 6 months, so invested for 6 months). Step 2: Find ratio X:Y:Z = 240,000:360,000:150,000. Divide by 30,000: ratio = 8:12:5. Step 3: Total parts = 8 + 12 + 5 = 25. Step 4: Z's profit = (5/25) × 9,000 = ₹1,800.

Question 10

A and B form a partnership. A invests ₹5,000 for 4 months, then adds ₹5,000 more (total ₹10,000) for the remaining 8 months. B invests ₹7,000 for 9 months, then withdraws ₹3,000 (leaving ₹4,000) for the remaining 3 months. If the total profit at the end of the year is ₹28,000, what is A's profit share?

Accepted Answer

Step 1: A's capital × time = (5,000 × 4) + (10,000 × 8) = 20,000 + 80,000 = 100,000. Step 2: B's capital × time = (7,000 × 9) + (4,000 × 3) = 63,000 + 12,000 = 75,000. Step 3: Ratio A:B = 100,000 : 75,000 = 4 : 3 (divide by 25,000). Step 4: Total parts = 4 + 3 = 7. Step 5: A's profit = (4/7) × 24,000 = 4 × 3,428.57... Hmm, not clean. Let me use profit = 28,000. Then A's profit = (4/7) × 28,000 = 4 × 4,000 = 16,000.

Question 11

In a partnership, M and N invest capital in the ratio 2:3. M invests for the entire year, but N invests for only 8 months. If M's profit is ₹8,000, what is N's profit?

Accepted Answer

Step 1: Let M's capital = 2x and N's capital = 3x. Step 2: M's capital × time = 2x × 12 = 24x. Step 3: N's capital × time = 3x × 8 = 24x. Step 4: Ratio of profits = 24x : 24x = 1 : 1. Step 5: Since M's profit = ₹8,000 and the ratio is 1:1, N's profit = ₹8,000.

Question 12

Three friends P, Q, and R invest in a venture in the ratio 3:4:5. After one year, their profits are in the ratio 6:8:10. If P's profit is ₹4,500, what is the total profit?

Accepted Answer

Step 1: Profit ratio is 6:8:10 = 3:4:5 (divide by 2). Step 2: This is the same as investment ratio! This means they invested for the same time period. Step 3: P's profit corresponds to 3 parts in the ratio 3:4:5. Step 4: If 3 parts = ₹4,500, then 1 part = ₹1,500. Step 5: Total parts = 3 + 4 + 5 = 12. Total profit = 12 × 1,500 = ₹18,000.

Question 13

P, Q, and R form a partnership where P and Q invest equal amounts, but P invests for 12 months while Q invests for only 8 months. R invests ₹15,000 more than P and invests for the entire year. If the profit is distributed in the ratio 3:2:5, what is P's initial investment?

Accepted Answer

Step 1: Let P = Q = x, R = x + 15,000. Step 2: Capital × Time: P = 12x, Q = 8x, R = 12x + 180,000. Step 3: Ratio = 3:2:5. Step 4: From 8x/(12x + 180,000) = 2/5: 40x = 24x + 360,000 → 16x = 360,000 → x = ₹22,500.

Question 14

X, Y, and Z form a partnership with capital contributions in the ratio 5:7:8. They agree that X will work as a manager and receive 10% of the profit as salary before profit distribution. The remaining profit is distributed in the ratio of their capital contributions. If the total profit is ₹1,20,000, what is X's total earning (salary + profit share)?

Accepted Answer

Step 1: X's salary = 10% of 1,20,000 = ₹12,000. Step 2: Remaining profit = 1,20,000 - 12,000 = ₹1,08,000. Step 3: Capital ratio X:Y:Z = 5:7:8. Total parts = 20. Step 4: X's share of remaining profit = (5/20) × 1,08,000 = (1/4) × 1,08,000 = ₹27,000. Step 5: X's total earning = 12,000 + 27,000 = ₹39,000.

Question 15

P and Q form a partnership where P contributes ₹80,000 and Q contributes ₹1,20,000. After 6 months, R joins with ₹1,00,000. If at the end of the year the profit is ₹1,44,000 and they decide to distribute it in the ratio of their capital contributions weighted by time, what is the difference between Q's and R's profit shares?

Accepted Answer

Step 1: Calculate capital × time for each partner. P: 80,000 × 12 = 960,000. Q: 120,000 × 12 = 1,440,000. R: 100,000 × 6 = 600,000. Step 2: Find ratio. Ratio = 960,000 : 1,440,000 : 600,000. Divide by 120,000: 8 : 12 : 5. Step 3: Total parts = 8 + 12 + 5 = 25. Step 4: Q's profit = (12/25) × 144,000 = 12 × 5,760 = ₹69,120. Step 5: R's profit = (5/25) × 144,000 = 5 × 5,760 = ₹28,800. Step 6: Difference = 69,120 - 28,800 = ₹40,320.

Question 16

Two partners, M and N, start a business. M invests ₹80,000 and N invests ₹1,20,000. After 4 months, M adds ₹40,000 and N withdraws ₹30,000. After another 4 months, M withdraws ₹20,000. At the end of the year, the profit is ₹1,08,000. What is the difference between M's and N's profit shares?

Accepted Answer

Step 1: Calculate M's weighted investment. Months 1-4: 80,000 × 4 = 320,000. Months 5-8: (80,000 + 40,000) × 4 = 120,000 × 4 = 480,000. Months 9-12: (120,000 - 20,000) × 4 = 100,000 × 4 = 400,000. Total M = 320,000 + 480,000 + 400,000 = 1,200,000. Step 2: Calculate N's weighted investment. Months 1-4: 1,20,000 × 4 = 480,000. Months 5-8: (1,20,000 - 30,000) × 4 = 90,000 × 4 = 360,000. Months 9-12: 90,000 × 4 = 360,000. Total N = 480,000 + 360,000 + 360,000 = 1,200,000. Step 3: Ratio M:N = 1,200,000 : 1,200,000 = 1:1. Step 4: M's profit = (1/2) × 1,08,000 = ₹54,000. N's profit = (1/2) × 1,08,000 = ₹54,000. Step 5: Difference = 54,000 - 54,000 = ₹0.

Question 17

P and Q start a business with capital in the ratio 7:5. After 6 months, P withdraws half of his capital and Q adds ₹20,000 more. If the profit at the end of the year is ₹33,600, and P's share is ₹16,800, what was Q's initial capital?

Accepted Answer

Step 1: Let P's initial capital = 7x and Q's initial capital = 5x. Step 2: P's weighted investment = 7x × 6 + (7x/2) × 6 = 42x + 21x = 63x. Step 3: Q's weighted investment = 5x × 6 + (5x + 20,000) × 6 = 30x + 30x + 120,000 = 60x + 120,000. Step 4: Profit ratio = P:Q = 63x : (60x + 120,000). Step 5: P's share = (63x / (63x + 60x + 120,000)) × 33,600 = 16,800. Step 6: 63x / (123x + 120,000) = 16,800 / 33,600 = 1/2. Step 7: 2 × 63x = 123x + 120,000 → 126x = 123x + 120,000 → 3x = 120,000 → x = 40,000. Step 8: Q's initial capital = 5x = 5 × 40,000 = ₹200,000.

Question 18

Three partners A, B, and C invest capital in the ratio 4:6:9. After 1 year, A adds ₹10,000, B withdraws ₹5,000, and C adds ₹15,000. In the second year, the profit is ₹1,44,000. If A's profit in the second year is ₹32,000, what was A's initial capital?

Accepted Answer

Step 1: Let initial capitals be A = 4x, B = 6x, C = 9x. Step 2: After changes, A = 4x + 10,000, B = 6x - 5,000, C = 9x + 15,000. Step 3: In year 2, profit ratio = (4x + 10,000) : (6x - 5,000) : (9x + 15,000). Step 4: A's share = 32,000 out of 1,44,000 total. Step 5: (4x + 10,000) / (4x + 10,000 + 6x - 5,000 + 9x + 15,000) = 32,000 / 1,44,000 = 2/9. Step 6: (4x + 10,000) / (19x + 20,000) = 2/9. Step 7: 9(4x + 10,000) = 2(19x + 20,000) → 36x + 90,000 = 38x + 40,000 → -2x = -50,000 → x = 25,000. Step 8: A's initial capital = 4x = 4 × 25,000 = ₹100,000.

Question 19

A and B enter into a partnership. A invests ₹45,000 for the entire year. B invests ₹40,000 for 9 months. After 1 year, they incur a loss of ₹9,000. If A's loss is ₹5,400, what is B's loss?

Accepted Answer

Step 1: Calculate weighted investments. A: 45,000 × 12 = 540,000. B: 40,000 × 9 = 360,000. Step 2: Find ratio A:B = 540,000 : 360,000 = 3 : 2. Step 3: Total parts = 3 + 2 = 5. Step 4: A's loss = (3/5) × 9,000 = 5,400 ✓ (matches given). Step 5: B's loss = (2/5) × 9,000 = 3,600.

Question 20

A, B, and C enter into a partnership. A invests ₹45,000 for 8 months, B invests ₹60,000 for 10 months, and C invests ₹50,000 for 12 months. If the total profit at the end of the year is ₹46,800, what is C's share of the profit?

Accepted Answer

Step 1: Calculate capital × time for each partner. A: 45,000 × 8 = 360,000. B: 60,000 × 10 = 600,000. C: 50,000 × 12 = 600,000. Step 2: Find the ratio A:B:C = 360,000 : 600,000 : 600,000 = 3 : 5 : 5. Step 3: Total parts = 3 + 5 + 5 = 13. Step 4: C's share = (5/13) × 46,800 = ₹18,000.

SSC CHSL Partnership

Partnership— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Partnership — Practice Questions

60-Second Revision — Partnership