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- Question
Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
Options- A. 5 : 7 : 8
- B. 20 : 49 : 64
- C. 38 : 28 : 21
- D. None of these
- Correct Answer
- 20 : 49 : 64
ExplanationLet their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.Then, 14x : 8y : 7z = 5 : 7 : 8.
Now, 14x = 5 ⟺ 98x = 40y ⟺ y = 49 x 8y 7 20 And, 14x = 5 ⟺ 112x = 35z ⟺ z = 112 x = 16 x. 7z 8 35 5 ∴ x : y : z = x : 49 x : 16 x = 20 : 49 : 64. 20 5
Partnership problems
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- 1. 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 - 2. 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.
- 3. 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 - 4. 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 - 5. 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 - 6. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.
Options- A. Rs. 1900
- B. Rs. 2660
- C. Rs. 2800
- D. Rs. 2840 Discuss
Correct Answer: Rs. 2660
Explanation:
For managing, A received = 5% of Rs. 7400 = Rs. 370.Balance = Rs. (7400 - 370) = Rs. 7030.
Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10
∴ B's share = Rs. ❨ 7030 x 14 ❩ = Rs. 2660. 37 - 7. A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew ¼ of his capital and B withdrew 1⁄5 of his capital. The gain at the end of 10 months was Rs. 760. A's share in this profit is:
Options- A. Rs. 330
- B. Rs. 360
- C. Rs. 380
- D. Rs. 430 Discuss
Correct Answer: Rs. 330
Explanation:
A : B = [ 4x x 3 + ❨ 4x - 1 x 4x ❩ x 7 ] : [ 5x x 3 + ❨ 5x - 1 x 5x ❩ x 7 ] 4 5 = (12x + 21x) : (15x + 28x)
= 33x :43x
= 33 : 43.
∴ A's share = Rs. ❨ 760 x 33 ❩ = Rs. 330. 76 - 8. Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
Options- A. Rs. 9,423
- B. Rs. 10,250
- C. Rs. 12,500
- D. Rs. 10,500 Discuss
Correct Answer: Rs. 10,500
Explanation:
Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.- 9. A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
Options- A. 32 years
- B. 36 years
- C. 40 years
- D. 48 years Discuss
Correct Answer: 40 years
Explanation:
Let the mother's present age be x years.Then, the person's present age = ❨ 2 x ❩ years. 5 ∴ ❨ 2 x + 8 ❩ = 1 (x + 8) 5 2 ⟹ 2(2x + 40) = 5(x + 8)
⟹ x = 40.
- 10. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
Options- A. 16 years
- B. 18 years
- C. 20 years
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 16 years
Explanation:
Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.Then, (6x + 6) + 4 = 11 (5x + 6) + 4 10 ⟹ 10(6x + 10) = 11(5x + 10)
⟹ 5x = 10
⟹ x = 2.
∴ Sagar's present age = (5x + 6) = 16 years.
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