Question 1

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. At the end of the year, the profit is ₹47,600. However, B withdraws ₹15,000 after 6 months (reducing his investment). What is A's share of the profit?

Accepted Answer

Step 1: Calculate capital × time for each partner. A: 45,000 × 8 = 360,000. B: (60,000 × 6) + (45,000 × 4) = 360,000 + 180,000 = 540,000. C: 50,000 × 12 = 600,000. Step 2: Find the ratio of investments: A:B:C = 360,000 : 540,000 : 600,000. Divide by 60,000: A:B:C = 6:9:10. Step 3: Total parts = 6 + 9 + 10 = 25. Step 4: A's share = (6/25) × 47,600 = 11,424.

Question 2

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. At the end of the year, the profit is ₹47,200. However, B withdraws ₹15,000 after 6 months (reducing his investment). What is A's share of the profit?

Accepted Answer

Step 1: Calculate capital × time for each partner. A: 45,000 × 8 = 360,000. B: (60,000 × 6) + (45,000 × 4) = 360,000 + 180,000 = 540,000. C: 50,000 × 12 = 600,000. Step 2: Find the ratio A:B:C = 360,000 : 540,000 : 600,000. Divide by 60,000 to simplify: 6 : 9 : 10. Step 3: Total parts = 6 + 9 + 10 = 25. Step 4: A's share = (6/25) × 47,200 = 0.24 × 47,200 = ₹11,328.

Question 3

A and B enter into a partnership. A invests ₹12,000 and B invests ₹18,000. After one year, the profit is ₹9,000. What is A's share of the profit?

Accepted Answer

Step 1: In a partnership, profit is divided in the ratio of capital invested. Step 2: Ratio of A's investment to B's investment = 12,000 : 18,000 = 2 : 3. Step 3: Total parts = 2 + 3 = 5. Step 4: A's share = (2/5) × 9,000 = ₹3,600.

Question 4

M and N invest capital in the ratio 5:7. They agree to share profits in the same ratio. If N receives ₹3,500 as profit, how much does M receive?

Accepted Answer

Step 1: Profit ratio M:N = 5:7. Step 2: Let M's profit = 5y and N's profit = 7y. Step 3: Given N's profit = ₹3,500, so 7y = 3,500, thus y = 500. Step 4: M's profit = 5y = 5 × 500 = ₹2,500.

Question 5

P and Q form a partnership. P invests ₹20,000 for 12 months and Q invests ₹25,000 for 8 months. If the profit is ₹11,000, how much profit does P receive?

Accepted Answer

Step 1: In a partnership with different time periods, profit is divided in the ratio of (Capital × Time). Step 2: P's contribution = 20,000 × 12 = 240,000. Step 3: Q's contribution = 25,000 × 8 = 200,000. Step 4: Ratio P : Q = 240,000 : 200,000 = 12 : 10 = 6 : 5. Step 5: Total parts = 6 + 5 = 11. Step 6: P's profit = (6/11) × 11,000 = ₹6,000.

Question 6

X, Y, and Z form a partnership with capital contributions in the ratio 2:3:5. If the total profit at the end of the year is ₹5,000, how much profit does Z receive?

Accepted Answer

Step 1: Capital ratio X:Y:Z = 2:3:5. Step 2: Total parts = 2 + 3 + 5 = 10. Step 3: Z's share of profit = (5/10) × 5,000 = (1/2) × 5,000 = ₹2,500.

Question 7

M and N entered into a partnership. M invested ₹50,000 for the entire year, while N invested ₹75,000 but only for 8 months. The profit earned is ₹13,000. What is N's share of the profit?

Accepted Answer

Step 1: M's capital-time contribution = 50,000 × 12 = 600,000. Step 2: N's capital-time contribution = 75,000 × 8 = 600,000. Step 3: Profit ratio M:N = 600,000:600,000 = 1:1. Step 4: N's share = (1/2) × 13,000 = ₹6,500.

Question 8

A and B enter into a partnership with capital investments of ₹15,000 and ₹25,000 respectively. If the profit at the end of the year is ₹8,000, what is B's share of the profit?

Accepted Answer

Step 1: Profit is distributed in the ratio of capital investments. Ratio of A's capital to B's capital = 15,000 : 25,000 = 3 : 5. Step 2: Total parts = 3 + 5 = 8. Step 3: B's share = (5/8) × 8,000 = ₹5,000.

Question 9

X, Y, and Z form a partnership with capital contributions in the ratio 2:3:5. If the total profit at the end of the year is ₹5,000, what is Z's profit share?

Accepted Answer

Step 1: Capital ratio X:Y:Z = 2:3:5. Step 2: Total parts = 2 + 3 + 5 = 10. Step 3: Z's share = (5/10) × 5,000 = ₹2,500.

Question 10

Two partners, M and N, invest capital in the ratio 3:4. They agree to share profits in the same ratio. If M's profit is ₹1,200, what is the total profit?

Accepted Answer

Step 1: Profit ratio M:N = 3:4 (same as capital ratio). Step 2: M's share = 3 parts, N's share = 4 parts. Step 3: Total parts = 3 + 4 = 7. Step 4: If M's profit (3 parts) = ₹1,200, then 1 part = ₹1,200 ÷ 3 = ₹400. Step 5: Total profit = 7 × ₹400 = ₹2,800.

Question 11

In a partnership, A and B's profit shares are in the ratio 3:2. If A's profit is ₹4,500, what is the total profit?

Accepted Answer

Step 1: Profit ratio A:B = 3:2. Step 2: Let A's profit = 3x and B's profit = 2x. Step 3: Given A's profit = ₹4,500, so 3x = 4,500, thus x = 1,500. Step 4: Total profit = 3x + 2x = 5x = 5 × 1,500 = ₹7,500.

Question 12

X, Y, and Z start a business with investments in the ratio 3 : 4 : 5. If the total profit at the end of the year is ₹24,000, what is Z's profit share?

Accepted Answer

Step 1: Investment ratio X : Y : Z = 3 : 4 : 5. Step 2: Total ratio parts = 3 + 4 + 5 = 12. Step 3: Z's share = (5/12) × 24,000 = ₹10,000.

Question 13

Three partners A, B, and C invest ₹2,000, ₹3,000, and ₹5,000 respectively. The profit is ₹3,000. If the profit is distributed equally among all three instead of by investment ratio, how much more does A receive?

Accepted Answer

Step 1: If profit is distributed equally, each partner gets ₹3,000 ÷ 3 = ₹1,000. Step 2: Based on investment ratio, A:B:C = 2,000:3,000:5,000 = 2:3:5. Step 3: Total parts = 10. A's rightful share = (2/10) × 3,000 = ₹600. Step 4: A receives ₹1,000 (equal distribution) but should receive ₹600. Difference = ₹1,000 - ₹600 = ₹400.

Question 14

Three partners A, B, and C invested capital in the ratio 3:4:5 and their profits were in the ratio 6:8:10. If the total profit is ₹5,400, what is C's profit?

Accepted Answer

Step 1: Capital ratio A:B:C = 3:4:5. Step 2: Profit ratio A:B:C = 6:8:10 = 3:4:5 (after simplification). Step 3: The profit ratio matches the capital ratio, confirming equal time periods. Step 4: Total parts = 3 + 4 + 5 = 12. Step 5: C's profit = (5/12) × 5,400 = ₹2,250.

Question 15

X and Y started a business with investments in the ratio 4:5. After one year, the profit earned is ₹18,000. If X's share of profit is ₹8,000, find Y's investment if X's investment was ₹40,000.

Accepted Answer

Step 1: Profit is distributed in the ratio of investments. X's profit share : Y's profit share = 8,000 : 10,000 = 4 : 5. Step 2: This confirms the investment ratio is 4:5. Step 3: If X's investment = ₹40,000 and ratio is 4:5, then Y's investment = (5/4) × 40,000 = ₹50,000.

Question 16

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 B'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: B's share = (11/20) × 2,000 = ₹1,100.

Question 17

A and B form a partnership where A invests ₹60,000 for 12 months and B invests ₹80,000 for 9 months. If the total profit is ₹7,900, what is A's share of the profit?

Accepted Answer

Step 1: When time periods differ, profit ratio = (Capital × Time) ratio. A's contribution = 60,000 × 12 = 720,000. Step 2: B's contribution = 80,000 × 9 = 720,000. Step 3: Ratio A:B = 720,000:720,000 = 1:1. Step 4: A's share = (1/2) × 7,900 = ₹3,950.

Question 18

P, Q, and R invested ₹20,000, ₹30,000, and ₹50,000 respectively in a partnership. The profit at the end of the year is ₹20,000. How much more profit does R get compared to P?

Accepted Answer

Step 1: Investment ratio P:Q:R = 20,000:30,000:50,000 = 2:3:5. Step 2: Total parts = 2 + 3 + 5 = 10. Step 3: P's profit share = (2/10) × 20,000 = ₹4,000. Step 4: R's profit share = (5/10) × 20,000 = ₹10,000. Step 5: Difference = 10,000 − 4,000 = ₹6,000.

Question 19

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 capital invested. 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 20

A, B, and C invest ₹15,000, ₹20,000, and ₹25,000 respectively for equal time periods. The profit earned is ₹12,000. What is the difference between C's and A's profit shares?

Accepted Answer

Step 1: Since time periods are equal, profit is divided in the ratio of capital invested. Step 2: Ratio A : B : C = 15,000 : 20,000 : 25,000 = 3 : 4 : 5. Step 3: Total parts = 3 + 4 + 5 = 12. Step 4: A's profit = (3/12) × 12,000 = ₹3,000. Step 5: C's profit = (5/12) × 12,000 = ₹5,000. Step 6: Difference = 5,000 - 3,000 = ₹2,000.

Question 21

In a partnership, A, B, and C's capital contributions are in the ratio 2:3:4. They decide that profits will be distributed in the ratio of their capital contributions. If B's profit is ₹4,500, what is the total profit?

Accepted Answer

Step 1: Capital ratio A:B:C = 2:3:4. Step 2: Since profit is distributed in the ratio of capital contributions, profit ratio = 2:3:4. Step 3: B's share corresponds to 3 parts. Step 4: If 3 parts = ₹4,500, then 1 part = ₹1,500. Step 5: Total parts = 2 + 3 + 4 = 9. Step 6: Total profit = 9 × 1,500 = ₹13,500.

Question 22

Two partners, S and T, invest capital in the ratio 3:2. They agree that S will receive 10% of the profit as a salary for managing the business, and the remaining profit will be divided in the ratio of their capital. If the total profit is ₹50,000, what is T's total share (including any salary if applicable)?

Accepted Answer

Step 1: S's salary = 10% of ₹50,000 = ₹5,000. Step 2: Remaining profit = ₹50,000 - ₹5,000 = ₹45,000. Step 3: Capital ratio S:T = 3:2, so total parts = 5. Step 4: S's share from remaining profit = (3/5) × ₹45,000 = ₹27,000. T's share from remaining profit = (2/5) × ₹45,000 = ₹18,000. Step 5: S's total = ₹5,000 (salary) + ₹27,000 (capital share) = ₹32,000. T's total = ₹18,000 (no salary). Therefore, T's total share = ₹18,000.

UP Police SI Partnership

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