Partnership problems
- 1. A, B and C do certain investments for time periods in the ratio of 2 : 1 : 8. At the and of the business term, they received the profits in the ratio of 3 : 4 : 2. Find the ratio of investments of A, B and C.
Options- A. 6 : 16 : 1
- B. 2 : 5 : 1
- C. 6 : 17 : 1
- D. 6 : 19 : 3 Discuss
Correct Answer: 6 : 16 : 1
Explanation:
Let required ratio of investments be
I1 : I2 : I3.
Ratio of investments = Ratio of profits
2I1 : I2 : 8I3 = 3 : 4 : 2
Taking first two terms of the ratio
(2I1) / I2 = 3/4
? I1 / I2 = 3/8 = 6/16
? I1 : I2 = 6 : 16
Taking last two terms of the ratio ,
I2 / (8I3) = 4/2
? I2/I3 = 16/1
? I2 : I3 = 16 : 1
? I1 : I2 : I3 = 6 : 16 : 1
- 2. A and B started a business by investing ? 20000 and ? 25000, respectively. After 4 months B left and C joined by investing ? 15000. At the end of the year, there was a profit of ? 23000 What is C's share?
Options- A. ? 8000
- B. ? 9000
- C. ? 6000
- D. ? 12000 Discuss
Correct Answer: ? 6000
Explanation:
A's share : B's share : C's share
= (20000 x 12) : (25000 x 4) : (15000 x 8)
= 240000 : 100000 : 120000
= 24 : 10 : 12 = 12 : 5 : 6
Let A's share = 12N
B's share = 5N
C's share = 6N
According to the question.
12N + 5N + 6N = 23000
? 23N = 23000
? N = 23000/23 = 1000
? C's share = 6N = 6 x 1000 = ? 6000
- 3. A and B started a business by investing ? 35000 and ? 20000, respectively. After 5 months B left the business and C joined the business with a sum of ? 15000. The profit earned at the end of year is ? 84125. What is the share of B in profit?
Options- A. ? 14133
- B. ? 15000
- C. ? 13460
- D. Couldn't be determined Discuss
Correct Answer: ? 13460
Explanation:
Ratio of equivalent capitals of A, B and C = (35000 x 12) : (20000 x 5) : (15000 x 7)
= 35 x 12 : 20 x 5 : 15 x 7
= 84 : 20 : 21
Let A's share = 84N
B's share = 20N
C's share = 21N
According to the question,
84N + 20N + 21N = 84125
? 125N = 84125
? N = 84125/125 = 673
? B's share = 20N = (20 x 673) = ? 13460
- 4. P and Q make a partnership, P invests ? 8000 for 8 months and Q remains in the business for 4 months. Out of the total profit, Q claims 2 / 7 of the profit. How much money was contributed by Y?
Options- A. ? 5000
- B. ? 5400
- C. ? 7400
- D. ? 6400 Discuss
Correct Answer: ? 6400
Explanation:
Q gets 2/7 of the profit.
? P gets(1 - 2/7) = 5/7 of the profit
? P : Q = 5/7 : 2/7 = 5 : 2
Let the contribution of Q be a.
Then, 8000 x 8 : a x 4 = 5 : 2
? 64000/4a = 5/2
? 20a = 128000
? a = 128000/20 = ? 6400
- 5. A and B invest ? 3000 and ? 4000, respectively in a business. A receives ? 10 per month out of the profit as a remuneration for running the business and the rest of the profit is divided in proportion to the investments. If in a year A totally receives ? 390, what does B receive?
Options- A. ? 630
- B. ? 360
- C. ? 480
- D. ? 380 Discuss
Correct Answer: ? 360
Explanation:
Let the annual profit be ? N Then, ? (N - 120) will be distributed between A and B as their shares of profit.
Ratio of profits = Ratio of investments So, A : B = 3000 : 4000 = 3 : 4
? A's share = 120 + (N - 120) x 3/7
? 120 + (N - 120) x 3/7 = 390
? (N - 120) x 3/7 = 390 - 120 = 270
? N - 120 = (270 x 7)/3 = 630
? B's share = 4/7 x (N - 120)
= (4/7) x 630 = ? 360
- 6. Amit and Brijesh started a business with initial investments in the ratio of 12 : 11 and their annual profits were in the ratio of 4 : 1. If Amit invested the money for 11 months, then for what time Brijesh invested the money?
Options- A. 9 months
- B. 3 months
- C. 5 months
- D. 10 months Discuss
Correct Answer: 3 months
Explanation:
Let investment of Amit = 12k
and investment of Brijesh = 11k
Let Brijesh invested the money for N months.
Then,
Amit's investment : Brijesh's investment
= (12k x 11) : (11k x N) = 132k : 11kN = 12 : N
? 12/N = 4/1 [ ? ratio of profit is 4 : 1]
? 4N = 12
? N = 12/4 = 3 months
Clearly, Brijesh invested money for 3 months.
- 7. Amitabh, Brijesh and Kamlesh enter a partnership with shares in the ratio of 7/2 : 4/3 : 6/5. After 4 months, Amitabh increases his share by 50% If the total profit at the end of the year be ? 21600, what will be the share of Brijesh in the profit?
Options- A. ? 8000
- B. ? 12000
- C. ? 4000
- D. ? 7000 Discuss
Correct Answer: ? 4000
Explanation:
Given. ratio = 7/2 : 4/3 : 6/5
= (7/2) x 30 : (4/3) x 30 : (6/5) x 30
= 105 : 40 : 36
Let investment of Amitabh = 105k
Investment of Kamlesh = 36k
Ratio of their investments
= [105k x 4 + 150% x8 of 105k] : (40k x 12) : (36k x 12)
= (420k + (150/100) x 105k x 8) : (480k) : (432k)
= (1680k) : (480k) : (432k)
= 35 : 10 : 9
? Brijesh's share
= (21600 x 10) / (35 + 10 + 9)
= (21600 x 10) / 54
= ? 4000
- 8. A and B started a joint business. A's investment was thrice the investment of B and the period of his investment was twice the period of investment of B. If B got ? 6000 as profit, then what will be the 20% of total profit?
Options- A. ? 5000
- B. ? 8400
- C. ? 3500
- D. ? 4500 Discuss
Correct Answer: ? 8400
Explanation:
Let investment of B be a for b months.
Then, A's investment = 3a for 2b months
? A : B = (3a x 2b) : (a x b) = 6ab : ab = 6 : 1
Let the total profit = m.
Then. m x 1/7 = 6000
? m = 6000 x 7 = ? 42000
? 20% of 42000 = ? 8400
- 9. A and B entered a partnership investing ? 16000 and ? 12000, respectively. After 3 months A takes out ? 5000, while B puts in ? 5000 more. After 3 months more. C joins the business with a capital of ? 21000. After a year, they earned a profit of ? 13200. By what value does the share of B exceeds the share of C?
Options- A. ? 1600
- B. ? 1800
- C. ? 2100
- D. ? 2300 Discuss
Correct Answer: ? 1800
Explanation:
A's share : B's share : C's share
= [16000 x 3 + (16000 - 5000) x 9] : [12000 x 3 + (12000 + 5000) x 9] : (21000 x 6)
= (16 x 3 + 11 x 9) : (12 x 3 + 17 x 9) : (21 x 6)
= 147 : 189 : 126
= 7 : 9 : 6
Hence, B's share exceeds C's share by = {13200/(7 + 9 + 6)} x (9 - 6)
= (13200 x 3)/22
= ? 1800
- 10. Two partners invest ? 125000 and ? 85000, respectively in a business and agree that 60% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets ? 600 more than the other, find the total profit made in the business.
Options- A. ? 8800
- B. ? 8885
- C. ? 8995
- D. ? 7875 Discuss
Correct Answer: ? 7875
Explanation:
The difference counts only due to 40% of the profit which was distributed according to their investments.
Let total profit = R.
40% of R is distributed in the ratio, 125000 : 85000 = 25 : 17
Share of 1st partner = 40% of R x25/(25 + 17)
= 40% of 25R/42 = (40/100) x (25R/42) = 5R/21
Share of 2nd partner
= 40% of 17R/42 = (40/100) x (17R/42) = 17R/105
Now according to the question
5R/21 - 17R/105 = 600
? R(25 - 17)/105 = 600
? R = (600 x 105)/8
= ? 7875
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