Partnership problems
- 1. Jagmohan, Rooplal and Pandeyji rented a video cassette for one week at a rent of Rs. 350. If they use it for 6 hours, 10 hours and 12 hours respectively. The rent to be paid by Pandeji is?
Options- A. Rs. 75
- B. Rs. 125
- C. Rs. 135
- D. Rs. 150 Discuss
Correct Answer: Rs. 150
Explanation:
Ratio of rent = 6 : 10 : 12 = 3 : 5 : 6
? Pandeyji has to pay = Rs. 350 x (6/14) = Rs. 150
- 2. A and B invest Rs. 3000 and Rs. 4000 in a business. A receives Rs. 10 per months out of the profit as a remuneration for running the business and the rest of profit is divided in proportion to the investment. In a year A totally receives Rs. 390. What does B receives?
Options- A. Rs. 630
- B. Rs. 360
- C. Rs. 480
- D. Rs. 380 Discuss
Correct Answer: Rs. 360
Explanation:
Total profit - Remuneration = Balance profit This balance profit is divided in proportion to their investment
? (Balance Profit of A) / (Balance Profit of B) = (Investment of A) / (investment of B)
? (390 - 10 x 12) / balance of Profit of B = 3000/4000 = 3/4
(Since remuneration of A is Rs. 10 per month)
? Balance profit of B = (4 x 270)/3 = Rs. 360
Since B does not get any remuneration, hence B receives Rs. 360 at the end of the year.
- 3. A starts a business with ? 4000. B joins him after 3 months with ? 8000. C puts a sum of ? 20000 in the business for 2 months only. At the end of year, the business gives a profit of ? 16800. How should the profit be divided amongst them?
Options- A. A = ? 5040 B = ? 7560, C = ? 4200
- B. A = ? 7560, B = ? 5040, C = ? 4200
- C. A = ? 4200, B = ? 7560, C = ? 5040
- D. A = ? 4200, B = ? 5040, C = ? 7560 Discuss
Correct Answer: A = ? 5040 B = ? 7560, C = ? 4200
Explanation:
A's share : B's share : C's share
= Ratio of product of investment and time period of investment
= 4000 x 12 : 8000 x (12 - 3) : 20000 x 2
= 4 x 12 : 8 x 9 : 20 x 2
= 6 : 9 : 5
Let,
A's share = 6N
B's share = 9N
C's share = 5N
According to the question,
6N + 9N + 5N = 16800
? 20N = 16800
? N = 16800/20 = 840
? A's share = 6N = 6 x 840 = ? 5040
B's share = 9N = 9 x 840 = ? 7560
C's share = 5N = 5 x 840 = ? 4200
- 4. P, Q and R start a business jointly. Twice the capital of P is equal to thrice the capital of Q and the capital of Q is four times the capital of R. Find the share of Q in an annual profit of ? 148500.
Options- A. ? 54000
- B. ? 64000
- C. ? 56000
- D. ? 55000 Discuss
Correct Answer: ? 54000
Explanation:
Let R's capital = 1
Then, Q's capital = 4
2 (P's capital) = 3 (Q's capital) = 3 x 4 = 12
? P's capital = 12/2 = 6
? P's share : Q's share : R's share = 6 : 4 : 1
Thus, Q's share profit = { 4/(6 + 4 + 1)} x 148500
= (4/11) x 148500
= 4 x 13500
= ? 54000
- 5. M, N and P invest ? 50000 for a business. M invests ? 4000 more than N and N invest ? 5000 more than P. Out of the total profit of ? 70000, what is the share received by M?
Options- A. ? 29400
- B. ? 30000
- C. ? 35000
- D. ? 40000 Discuss
Correct Answer: ? 29400
Explanation:
Let investment of P = ? K
Then, investment of N of = ? (K + 5000)
and investment of M = (K + 5000) + 4000 = ? (K + 9000)
According to the question.
K + (K + 5000) + (K + 9000) = 50000
? 3K + 14000 = 50000
? 3K = 50000 - 14000 = 36000
? K = 36000/3 = 12000
Clearly, investment of P = ? 12000
Investment of N = (K + 5000) = 12000 + 5000 = ? 17000
Investment of M = (K + 9000) = 12000 + 9000 = ? 21000
M's share : N's share : P's share = 21000 : 17000 : 12000
= 21 : 17 : 12
Hence, M's share = [21/(21 + 17 + 12 )] x 70000
= (21/50) x 70000 = ? 29400
- 6. P, Q and R hire a meadow for ? 2920. P puts 10 cows for 20 days, Q puts 30 cows for 8 days and R puts 16 cows for 9 days. Find the rent paid by R.
Options- A. ? 735
- B. ? 820
- C. ? 575
- D. ? 720 Discuss
Correct Answer: ? 720
Explanation:
Ratio of rents to be paid by P, Q and R Ratio of monthly equivalent
= (10 x 20) : (30 x 8) : (16 x 9)
= 200 : 240 : 144 = 25 : 30 : 18
Hence R's share
= [18/(25 + 30 + 18)] x 2920
= (18/73) x 2920
= 18 x 40
= ? 720
- 7. A, B and C enter into a partnership. A invests some amount at the beginning, B invests double the amount of A after 6 months and C invests thrice the amount of A after 8 months. If the annual profit be ? 54000, find the C's share.
Options- A. ? 3000
- B. ? 18000
- C. ? 15000
- D. ? 21000 Discuss
Correct Answer: ? 18000
Explanation:
Let investment of A = N,
Investment of B = 2N,
Investment of C = 3N,
? A's share : B's share : C's share
= (N x 12) : (2N x 6) : (3N x 4)
= 12N : 12N : 12N
= 1 : 1 : 1
? C's share = [1/(1 + 1 + 1)] x 54000
= (1/3) x 54000 = ? 18000
- 8. A. B and C together start a business. B invests of 1/6 of the total capital while investments of A and C are equal. If the annual profit on this investment is ? 33600, find the difference between the profits of B and C.
Options- A. ? 8400
- B. ? 7200
- C. ? 6000
- D. ? 9600 Discuss
Correct Answer: ? 8400
Explanation:
Given, Investment of B = 1/6 of total capital
? Investments of A and C each = 1/2(1 - 1/6) of total capital
= (1/2) x (5/6) of total capital
= (5/12) of total capital
Now. A's share : B's share : C's share = (5/12) : (1/6) : (5/12) = 5 : 2 : 5
Let A's share = 5N
B's share = 2N
C's share = 5N
According to the question.
5N + 2N + 5N = 33600
? 12N = 33600
? N = 33600/12 = 2800
? Difference in the profits of B and C
= 5N - 2N = 3N = 3 x 2800 = ? 8400
- 9. A and B invest in a business in the ratio of 3 : 2. If 5% of the total profit goes to a charity and A's share is ? 4275, then what will be the total profit?
Options- A. ? 8000
- B. ? 7700
- C. ? 7500
- D. ? 6500 Discuss
Correct Answer: ? 7500
Explanation:
Let total profit = N
Paid to charity = 5% of N = (5 x N)/100 = N/20
? Balance profit = N - N/20 = 19N/20
? A's share = (19N/20) x (3/5) = 57N/100
According to the question.
57N/100 = 4275
? N = (4275 x 100)/57 = 7500
Hence. total profit = ? 7500
- 10. A and B together start a business by investing in the ratio of 4 : 3. If 9% of the total profit goes to charity and A's share is ? 1196, find the total profit.
Options- A. ? 2300
- B. ? 4435
- C. ? 2093
- D. ? 2700 Discuss
Correct Answer: ? 2300
Explanation:
Let total profit = N
Paid to charity = 9% of N = 9N/100
? Balance profit = N - (9N/100) = 91N/100
? A's share = [4/(4 + 3)] x (91N/100) = (4/7) x (91N/100)
According to the question,
(4/7) x (91N/100) = 1196
? N = (1196 x 7 x 100)/(4 x 91) = ? 2300
Hence, total profit = ? 2300
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