Quantitative Aptitude :: Partnership Formulas

Partnership Questions and Answers

Awards and Honors
IBPS Model Paper
SBI Model Paper
Bank Exam Model Paper
Introduction
When two or more than two persons run a business jointly, they are called 'partners' in the business and the deal
between them is known as 'Partnership'.
Partnership is of two kinds
1. Simple partnership and 
2. Compound partnership

1. Simple partnership When investments of all the partners are for the same period of time, the 
   profit or loss is distributed among the partners in the ratio of their original investments.
   Suppose A and B invest p and q respectively for a year in a business then, at the end of the year
   Share of A's profit (Loss) : Share of B's profit(Loss) = p:q

2. Compound partnership When investments of all the partners are for different period of time then, equivalent 
   capitals are calculated for a unit of time and profit or loss is divided in the ratio of the product of 
   time and investment.
   Suppose A and B invest p and q for x months and y months respectively, then 
   Share of A's profit (loss) : Share of B's profit (Loss) = px : qy 
   Partners are of two types 
   1. Working partners, and 
   2. Sleeping partner 
   1. Working partner A partner who manages the business is called as a 'working partner'.
   2. Sleeping partner A partner who only invests the money is called a 'sleeping partner'.
 

Solved Examples

 Example 1  A and B stared a business with capitals of 25000 rupees and 40000 rupees respectively.
 Find the ratio of the shares of A and B.
 Solution : Ratio of shares of A and B = Ratio of their investments.
                                       = 25000 : 40000 = 5 : 8 
                                                                           
Example 2   A, B and C stared a business by investing Rs.28000, Rs.35000 and Rs.14000 respectively.
At the end of the year, they got a total profit of Rs.5225. Find A's share.
Solution : Ratio of shares of A, B and C = Ratio of their investments
                                         = 28000 : 35000 : 14000 = 4 : 5 : 2 
                        A's share = Rs.[(4/11) × 5225] = Rs.1900
Example 3 : A started a business investing Rs.30000. After 2 months B joined him with a capital of Rs.45000.
After another 2 months C joined them with a capital of Rs.67500. At the end of the year, they made a profit
of Rs.13500. Find the share of B.
Solution : Clearly, A invested his capital for 12 months. B for 10 months and C for 8 months.
So, ratio of their capital
                          = (30000 × 12) : (45000 × 10) : (67500 × 8) 
                                                  = 360000 : 450000 : 540000
                                                  = 4 : 5 : 6 
                    B's Share = Rs.[(5/15) × 13500] = Rs.4500 
Example 4 : A, B and C start a business each investing Rs.16000. After 3 months A withdrew Rs.2000. B withdrew
Rs.4000 and C invests Rs.8000 more. At the year a total profit Rs.41580 was made. Find the share of A.
Solution : Ratio of capitals of A, B and C 
               = (16000 × 3 + 14000 × 9) : (16000 × 3 + 12000 × 9) : (16000 × 3 + 24000 × 9)
               = 174000 : 156000 : 264000 
               = 29 : 26 : 44 
      A's Share = Rs.(29/99 × 41580) = Rs.12180