Partnership
Important Formulae
Ratio of Divisions of Gains:
1.When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.
Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year:
(A's share of profit) : (B's share of profit) = x : y
2. When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time). Now gain or loss is divided in the ratio of these capitals.
Suppose A invests Rs. x for p months and B invests Rs. y for q months then,
(A's share of profit) : (B's share of profit)= xp : yq
General Tips
1. Partnership:
When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership.
2. Working and Sleeping Partners:
A partner who manages the the business is known as a working partner and the one who simply invests the money is a sleeping partner.
Example 1:
A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After six months, C joined them with Rs.20,000. What will be B's share in the total profit of Rs.25,000 earned at the end of 2 years from the starting of the business?
Solution:
A : B : C =(20000×24):(15000×24):(20000×18)
=>4 :3 :3
B's share =Rs.(25000×3/10)
= Rs.7500.
Example 2:
Arun, Kamal and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?
Solution:
Arun : Kamal : Vinay = (8,000 x 6) : (4,000 x 8) : (8,000 x 8)
Arun : Kamal : Vinay = 48 : 32 : 64
Arun : Kamal : Vinay = 3 : 2 : 4
Kamal's share = Rs.4005 *(2/9)= Rs. 890
Example 3:
A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.
Solution
For managing, A received = 5% of Rs. 7400 = Rs. 370
Balance = Rs. (7400 - 370) = Rs. 7030
Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10
B's share = Rs.7030*(14/37) = = Rs.2660
Example 3:
X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 3. If X invested Rs.40,000. the amount invested by Y is
Solution
Suppose Y invested Rs.y
Then, 40000 /y = 2 / 3
=> y=(40000×3 / 2)
=> y=60000
