# Chapter 9: PARTNERSHIP THEORY

### Introduction

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.

### Quiz

Score more than 80% marks and move ahead else stay back and read again!