PARTNERSHIP :- When two or more persons jointly start a business with an objective to earn money, this is called partnership.
These persons are called partners and the money invested in the business is known as capital.
Case 1. :- When the partners invest different amount of money for equal interval of time, then profit or loss is divided in the ratio of their investments.
Example :- Vimal and Pawan invested Rs 4800 and Rs 5400 respectively in a business. If the profit at the end of the year was Rs 5185, find the profit of each of them?
Sol.
Vimal's capital : Pawan's capital = 4800 :5400
= 8 : 9
$\therefore$ Vimal's profit : Pawan's profit = 8 : 9
Sum of ratios = 8 + 9 = 17
$\because$ Total profit = Rs 5185
$\therefore$ Vimal's profit = $\frac{8}{17}\times 5185$
= Rs 2440
and, Pawan's profit = $\frac{9}{17}\times 5185$
= Rs 2745
Case 2. :- When equal capital is invested for different time periods, the profit or loss is distributed in the ratio of time period.
Example :- Anil started a business by investing Rs 25000, 3 months later Sunil joined the business by investing Rs 25000. At the end of the year Anil got Rs 1000 more than Sunil out of the profit. Find the total profit?
Sol.
Anil invested for 12 months
Sunil invested for ( 12 - 3 ) = 9 months
$\because$ The capital of both are equal
$\therefore$ Ainl's profit : Sunil's profit = 12 : 9
Difference of the number of ratio = 4 - 3 = 1
Sum of the number of ratio = 4 + 3 = 7
Difference of profits of Anil and Sunil = Rs 1000
$\therefore$ Total profit = $\frac{7}{1}\times 1000$
= Rs 7000
Case 3. :- When different capitals are invested for different periods of time then, the profit or loss can be distributed by converting the capital on the basis of a common period or by converting the time period on the basis of a common capiatl.
Example :- A and B entered into a pertnership by investing Rs 14000 and Rs 18000 respectively. A withdrew his money after 4 months. If the total profit at the end is Rs 12240, find the profit of each?
Sol.
A's Rs 14000 for 4 months = 14000 $\times$ 4
= Rs 56000 for one month
B's Rs 18000 for 12 months = 18000 $\times$ 12
= Rs 216000 for one month
ON THE BASIS OF COMMON TIME
A's capital : B's capital = 56000 : 216000
= 7 : 27
Sum of ratio = 7 + 27 = 34
Total profit = Rs 12240
A's profit = $\frac{7}{34}\times 12240$
= Rs 2520
B's profit = $\frac{27}{34}\times 12240$
= Rs 9720
These persons are called partners and the money invested in the business is known as capital.
Case 1. :- When the partners invest different amount of money for equal interval of time, then profit or loss is divided in the ratio of their investments.
Example :- Vimal and Pawan invested Rs 4800 and Rs 5400 respectively in a business. If the profit at the end of the year was Rs 5185, find the profit of each of them?
Sol.
Vimal's capital : Pawan's capital = 4800 :5400
= 8 : 9
$\therefore$ Vimal's profit : Pawan's profit = 8 : 9
Sum of ratios = 8 + 9 = 17
$\because$ Total profit = Rs 5185
$\therefore$ Vimal's profit = $\frac{8}{17}\times 5185$
= Rs 2440
and, Pawan's profit = $\frac{9}{17}\times 5185$
= Rs 2745
Case 2. :- When equal capital is invested for different time periods, the profit or loss is distributed in the ratio of time period.
Example :- Anil started a business by investing Rs 25000, 3 months later Sunil joined the business by investing Rs 25000. At the end of the year Anil got Rs 1000 more than Sunil out of the profit. Find the total profit?
Sol.
Anil invested for 12 months
Sunil invested for ( 12 - 3 ) = 9 months
$\because$ The capital of both are equal
$\therefore$ Ainl's profit : Sunil's profit = 12 : 9
Difference of the number of ratio = 4 - 3 = 1
Sum of the number of ratio = 4 + 3 = 7
Difference of profits of Anil and Sunil = Rs 1000
$\therefore$ Total profit = $\frac{7}{1}\times 1000$
= Rs 7000
Case 3. :- When different capitals are invested for different periods of time then, the profit or loss can be distributed by converting the capital on the basis of a common period or by converting the time period on the basis of a common capiatl.
Example :- A and B entered into a pertnership by investing Rs 14000 and Rs 18000 respectively. A withdrew his money after 4 months. If the total profit at the end is Rs 12240, find the profit of each?
Sol.
A's Rs 14000 for 4 months = 14000 $\times$ 4
= Rs 56000 for one month
B's Rs 18000 for 12 months = 18000 $\times$ 12
= Rs 216000 for one month
ON THE BASIS OF COMMON TIME
A's capital : B's capital = 56000 : 216000
= 7 : 27
Sum of ratio = 7 + 27 = 34
Total profit = Rs 12240
A's profit = $\frac{7}{34}\times 12240$
= Rs 2520
B's profit = $\frac{27}{34}\times 12240$
= Rs 9720
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