- Home
- Partnership Theory

# PARTNERSHIP THEORY

When A and B are partners and both invest in a ratio say x:y but at the same time then their ratio of profits sharing is same as their investment ratio i.e. **x:y.**

However if A invests ‘x’ amount for ‘p’ months and B invests ‘y’ amount for ‘q’ months then their share in profits is:

A’s share : B’s share = x * p : y * q |

**Q.** If A invests 1,20000 B invests 1,35000 and C invests 150000 then find their share in profits if profit is 56700.

**A.** Ratio of their investments is 8:9:10 since we can divide by 15 after cancelling zeros. Then A’s share is 8/27 as 8/8+9+10 and similarly B’s share is 9/27 and C’s share is 10/27. Using these we can get their final amount.

**Q.**Alfred started a business investing Rs. 45,000. After 3 months, Peter joined him with a capital of Rs. 60,000. After another 6 months, Ronald joined them with a capital of Rs. 90,000. At the end of the year, they made a profit of Rs. 16,500. Find the share of each.

**A.** Alfred’s investment = 45000 * 12 months; Peter’s investment = 60000 * 9 months; Ronald’s investment = 90000 * 6 months;

A:B:C = 45*12 : 60*9: 90*6 = 3*12:4*9:6*6 = 2:2:1 so Alfred’s share is 2/5, Peter’s share is 2/5 and Ronald’s is 1/5. Use this to get their shares.

**Q. **A, Band C start a business each investing Rs. 20,000. After 5 months A withdrew Rs.6000 B withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the share of each.

**A. **A’s share = 20000*5 + 14000*7

B’s share = 20000*5 + 16000 * 7 and C’s share = 20000*5 + 26000*7.

A:B:C = 205:212:282

**Q.** A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 6600. What is the share of B ?

**A. **Let C’s share be ‘x’ and so B gets 2x/3 and then A gets 2x so their ratio is

A:B:C = 2: (2/3) : 1, multiplying by 3 throughout we get

A:B:C = 6:2:3

**Q.** A invested Rs. 76,000 in a business. After few months, B joined him Rs. 57,000. At the end of the year, the total profit was divided between them in ratio 2 : 1. After bow many months did B join?

**A.** A’s share = 76000*12 and B’s share is 57000 * ‘x’

A:B = 76*12 : 57 * x = 2:1 we get x=8 months.

So B invested for 8 months hence he joined after 4 months.

**Q.** A, B and C enter into a partnership by investing in the ratio of 3 : 2 : 4. After 1 year, B invests another Rs. 2,70,000 and C, at the end of 2 years, also invests Rs.2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find initial investment of each.

**A.** The initial investment’s of A,B,C be 3x, 2x and 4x.

A’s share 3x * 36, B’s share is 2x * 12 + 270000 * 24, C’s share is 4x * 24 + 270000 * 12.

A:B:C = 3:4:5 using this ratio we can get their shares.

Q1: When A and B are partners and both invest in a ratio say 3:1 so the profit of A out of 100 is

75

25

40

60

ANS.75

Q2: If A invests 1,20000 B invests 1,35000 and C invests 150000 then find A’s share in profits if profit is 56700.

16800

17800

18800

19800

ANS.16800

Q3: Alfred started a business investing Rs. 45,000. After 3 months, Peter joined him with a capital of Rs. 60,000. After another 6 months, Ronald joined them with a capital of Rs. 90,000. At the end of the year, they made a profit of Rs. 16,500. Find the ratio of share of each

1:2:2

2:1:2

2:2:1

1:2:3

ANS.2:2:1

Q4: A, Band C start a business each investing Rs. 20,000. After 5 months A withdrew Rs.6000 B withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the ratio of share of each.

205:212:282

205:200:282

200:212:282

205:212:280

ANS.205:212:282

Q5: A invested Rs. 76,000 in a business. After few months, B joined him Rs. 57,000. At the end of the year, the total profit was divided between them in ratio 2 : 1. After how many months did B join?

3

4

5

6

ANS.4