Partnership problems
- 1. Four milkmen rented a pasture. A grazed 18 cows for 4 months, B grazed 25 cows for 2 months, C grazed 28 cows for 5 months and D grazed 21 cows for 3 months. If A's share of rent is ? 720, what will be the total rent of the pasture?
Options- A. ? 1650
- B. ? 3250
- C. ? 3500
- D. ? 3000 Discuss
Correct Answer: ? 3250
Explanation:
Ratio of rents of A, B, C and D
= (18 x 4) : (25 x 2) : (28 x 5) : (21 x 3)
= 72 : 50 : 140 : 63
Let the total rent be N.
Then, A's share = [72N / (72 + 50 + 140 + 63)] = 72N/325
According to the question. 72N/325 = 720
? N = (720 x 325)/72 = 3250
? Total Rent = ? 3250
- 2. A, B and C invested their capitals in the ratio of 5 : 6 : 8. At the end of the business, they received the profits in the ratio of 5 : 3 : 1. Find the ratio of time for which they contributed their capitals. `
Options- A. 12 : 9 : 7
- B. 25 : 18 : 8
- C. 5 : 6 : 8
- D. 8 : 4 : 1 Discuss
Correct Answer: 8 : 4 : 1
Explanation:
Here, p1 : p2 : p3 = 5 : 3 : 1 and x1 : x2 : x3 = 5 : 6 : 8
According to the formula,
Required ratio = p1/x1 : p2/x2 : p3/x3
= 5/5 : 3/6 : 1/8
= 1 : 1/2 : 1/8 = 8 : 8/2 : 8/8 = 8 : 4 : 1
- 3. Sonu invested 10% more than the investment of Mona and Mona invested 10% less than the investment of Raghu. If the total investment of all the three persons is ? 5780, find the investment of Raghu.
Options- A. ? 2010
- B. ? 2000
- C. ? 2100
- D. ? 2210 Discuss
Correct Answer: ? 2000
Explanation:
Let share of Raghu be 100. Then share of Mona = 90 and share of Sonu = 99
Sonu : Mona : Raghu = 99 : 90 : 100
? Investment of Raghu = [100/(99 + 90 + 100)] x 5780
= (100/289) x 5780 = ? 2000
- 4. A, B and C entered into partnershp in a business. A got 3/5 of the profit. B and C distributed the remaining profit equally. if C got ? 400 less than A, the total profit was
Options- A. ? 1600
- B. ? 1200
- C. ? 1000
- D. ? 800 Discuss
Correct Answer: ? 1000
Explanation:
Let the total profit be ? N,
Then, A's share in profit = ? 3N/5
Remaining profit = N - 3N/5 = (5N - 3N) / 5 = 2N/5
? B's share in profit = ? N/5
C's share in profit = ? N/5
According to the question,
(3N/5 - N/5) = 400
2N/5 = 400; N = (400 x 5)/2 = ? 1000
- 5. A began a business with ? 2250 and was joined afterwards by B with ? 2700. If the profits at the end of the year were divided in the ratio of 2 : 1, after how much time B joined the business?
Options- A. 5 months
- B. 6 months
- C. 3 months
- D. 7 months Discuss
Correct Answer: 7 months
Explanation:
Let B remained in the business for N months. Then,
A : B = (2250 x 12) : (2700 x N)
? 2 : 1 = (27000 : 2700N) = (10 : N)
? 10/N = 2/1 [ ? Ratio of profit is 2 : 1]
? 2N = 10
? N = 10/2 = 5
Clearly, B joined after (12 - 5) = 7 months.
- 6. A, B and C invested capitals in the ratio of 4 : 6 : 9. At the end of the business term, they received the profit in the ratio of 2 : 3 : 5. Find the ratio of their time for which they contributed their capitals.
Options- A. 1 : 1 : 9
- B. 2 : 2 : 9
- C. 10 : 10 : 9
- D. 9 : 9 : 10 Discuss
Correct Answer: 9 : 9 : 10
Explanation:
Here, P1 : P2 : P3 = 2 : 3 : 5 [profit's ratio]
and x1 : x2 : x3 = 4 : 6 : 9 [investment's ratio]
According to the rule,
Required ratio = P1/x1 : P2/x2 : P3/x3
= 2/4 : 3/6 : 5/9
= 1/2 : 1/2 : 5/9 = 9 : 9 : 10
- 7. Aarti, Vinita and Kamla became partners in a business by investing money in the ratio of 5 : 7 : 6. Next year, they increased their investments by 26%, 20% and 15%, respectively. In what ratio should profit earned during 2nd year be distributed?
Options- A. 21 : 28 : 23
- B. 23 : 28 : 21
- C. 28 : 23 : 21
- D. 35 : 41 : 7 Discuss
Correct Answer: 21 : 28 : 23
Explanation:
Let investment of Aarti during first year = 5a
Investment of Vinita during first year = 7a
Investment of kamla during first year = 6a
Then, their investments during second year are
? (126/100) x 5a : (120/100) x 7a : (115/100) x 6a
= 630 : 840 : 690 = 21 : 28 : 23
- 8. Anil is an active and Vimal is a sleeping partner in a business. Anil invests ? 12000 and Vimal invests ? 20000. Anil receives 10% profit for managing, the rest being divided in proportion to their capitals. Out of the total profit of ? 9000, the money received by Anil is
Options- A. ? 4500
- B. ? 4800
- C. ? 4600
- D. ? 3937.5 Discuss
Correct Answer: ? 3937.5
Explanation:
For management, money received by Anil = 10% of 9000 = ? 900
Balance = ? (9000 - 900) = ? 8100
Now, ratio of investments =12000 : 20000 = 3 : 5
? Anil's share = ? 8100 x 3/(3 + 5)
= ? 8100 x 3/8 = ? 3037.50
? Amount received by Anil = ? 900 + 3037.50
= ? 3937.50
- 9. Aayush and Babloo are partners in a business. Aayush contributes 1/4 of the capital for 15 months and Babloo received 2/3 of the profit. How long Babloo's money was used?
Options- A. 10 months
- B. 9 months
- C. 11 months
- D. 7 months Discuss
Correct Answer: 10 months
Explanation:
Let the total capital be ? R and Babloo's money is used for N months.
Capital of Aayush = R/4
? Capital of Babloo = (R - R/4) = 3R/4
Ratio of investments of Aayush and Babloo
= (R/4) x 15 : (3R/4 x b) = 15/4 : 3N/4 = 5 : N
Ratio of profits of Aayush and Babloo = (1/3) : (2/3) = 1 : 2
? 5/N = 1/2
? N = 10 months
Hence, Babloo's money was used for 10 months.
- 10. A and B started a business with ? 20000 and ? 35000 respectively. They agreed to share the profit in the ratio of their capital. C joins the partnership with the condition that A, B and C will share profit equally and pays ? 220000 as premium for this, to be shared between A and B. This is to be divided between A and B in the ratio of?
Options- A. 10 : 1
- B. 1 : 10
- C. 9 : 10
- D. 10 : 9 Discuss
Correct Answer: 10 : 1
Explanation:
Ratio of total capital of A and B = 20000 x 12 : 35000 x 12
= 240000 : 420000
Now, C gives ? 220000 to both to make the capital equal.
? A's capital : B's capital = 240000 + 200000 : 420000 + 200000
= 440000 : 440000
If A takes ? 200000 and B takes ? 20000 from C, then both have the equal capital
? Required ratio of divided amount
= 200000 : 20000
= 20 : 2 = 10 : 1
Hence. A and B should divide the amount in the ratio of 10 : 1.
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