Partnership problems
- 1. A, B and C enter into a partnership in the ratio 7⁄2 : 4⁄3 : 6⁄5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then B's share in the profit is:
Options- A. Rs. 2100
- B. Rs. 2400
- C. Rs. 3600
- D. Rs. 4000 Discuss
Correct Answer: Rs. 4000
Explanation:
| Ratio of initial investments = | ❨ | 7 | : | 4 | : | 6 | ❩ | = 105 : 40 : 36. |
| 2 | 3 | 5 |
Let the initial investments be 105x, 40x and 36x.
| ∴ A : B : C = | ❨ | 105x x 4 + | 150 | x 105x x 8 | ❩ | : (40x x 12) : (36x x 12) |
| 100 |
= 1680x : 480x : 432x = 35 : 10 : 9.
| Hence, B's share = Rs. | ❨ | 21600 x | 10 | ❩ | = Rs. 4000. |
| 54 |
- 2. A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?
Options- A. Rs. 7500
- B. Rs. 8000
- C. Rs. 8500
- D. Rs. 9000 Discuss
Correct Answer: Rs. 9000
Explanation:
Let B's capital be Rs. x.
| Then, | ❨ | 3500 x 12 | = | 2 | ❩ |
| 7x | 3 |
⟹ 14x = 126000
⟹ x = 9000.
- 3. A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
Options- A. Rs. 7500
- B. Rs. 9000
- C. Rs. 9500
- D. Rs. 10,000 Discuss
Correct Answer: Rs. 7500
Explanation:
A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
| ∴ B's share = Rs. | ❨ | 25000 x | 3 | ❩ | = Rs. 7,500. |
| 10 |
- 4. Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs.. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
Options- A. 7 : 6 : 10
- B. 12 : 15 : 16
- C. 42 : 45 : 56
- D. Cannot be determined Discuss
Correct Answer: 12 : 15 : 16
Explanation:
Aman : Rakhi : Sagar = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24) = 12 : 15 : 16.
- 5. A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
Options- A. 3 : 5 : 2
- B. 3 : 5 : 5
- C. 6 : 10 : 5
- D. Data inadequate Discuss
Correct Answer: 6 : 10 : 5
Explanation:
Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.
- 6. Arun, Kamal and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?
Options- A. Rs. 890
- B. Rs. 1335
- C. Rs. 1602
- D. Rs. 1780 Discuss
Correct Answer: Rs. 890
Explanation:
Arun : Kamal : Vinay = (8,000 x 6) : (4,000 x 8) : (8,000 x 8)
= 48 : 32 : 64
= 3 : 2 : 4.
| ∴ Kamal's share = Rs. | ❨ | 4005 x | 2 | ❩ | = Rs. 890. |
| 9 |
- 7. A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is:
Options- A. Rs. 1425
- B. Rs. 1500
- C. Rs. 1537.50
- D. Rs. 1576 Discuss
Correct Answer: Rs. 1500
Explanation:
Let the total profit be Rs. 100.
| After paying to charity, A's share = Rs. | ❨ | 95 x | 3 | ❩ | = Rs. 57. |
| 5 |
If A's share is Rs. 57, total profit = Rs. 100.
| If A's share Rs. 855, total profit = | ❨ | 100 | x 855 | ❩ | = 1500. |
| 57 |
- 8. A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
Options- A. Rs. 45
- B. Rs. 50
- C. Rs. 55
- D. Rs. 60 Discuss
Correct Answer: Rs. 45
Explanation:
A : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9.
| ∴ C's rent = Rs. | ❨ | 175 x | 9 | ❩ | = Rs. 45. |
| 35 |
- 9. A began a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
Options- A. 4 months
- B. 5 months
- C. 6 months
- D. 8 months Discuss
Correct Answer: 8 months
Explanation:
Suppose B joined for x months. Then,
| Then, | ❨ | 85000 x 12 | = | 3 | ❩ |
| 42500 x x | 1 |
| ⟹ x = | ❨ | 85000 x 12 | ❩ | = 8. |
| 42500 x 3 |
So, B joined for 8 months.
- 10. A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:
Options- A. Rs. 8400
- B. Rs. 11,900
- C. Rs. 13,600
- D. Rs. 14,700 Discuss
Correct Answer: Rs. 14,700
Explanation:
Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
⟹ 3x = 36000
⟹ x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
| ∴ A's share = Rs. | ❨ | 35000 x | 21 | ❩ | = Rs. 14,700. |
| 50 |
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