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Partnership:

Concept of Partnership and Examples:

When two or more people run a business jointly and they also agree to share profit and losses between them then that is called partnerships and all these people are called partners.

Capital:

The amount invested by the partners to start any business is known as capital.

Equivalent Capital:

When the capital is different for different partners and the time period is also different then we need to multiply the investment with the time period. The product is called equivalent capital or money time capital.

Few rules of partnerships:

Case 1:

If the partners invest the same amount for the same period of time then the profit and loss will be shared equally.

Example:

Ram and Madhu started a business by investing 25000 each. After one year profit is 9880 Rs. Find the share of each.

Solution:

In this case, investment is the same, and also the time period is the same. So, profit will be shared equally.

So, the share of each is (9880 ÷ 2) Rs = 4940 Rs.

Case 2:

If the partners invest a different amount for the same period of time then the profit and loss will be shared in the ratio of their investment.

Example:

Varun and Tarun started a business by investing 56000 Rs. And 40000 Rs. Find the share of each out of an annual profit of 24000 Rs.

Solution:

Case 3:

If the partners invest the same amount for the different time periods. Then the profit and loss will be shared among the time period for which the sums were invested.

Example:

A Starts some business with Rs 60,000. After 2 months B joins him with Rs 60,000. After 2 months of joining B, C joins the business with Rs 60,000. Find the share of each out of an annual profit of Rs 21,000.

Solution:

Here the investment is the same but the time period is different so the profit will be shared as per the ratio of their time period of investment.

The ratio of the time period of A’s, B’s, C’s investment is 12 months : 10 months : 8 months  = 6 : 5 : 4

Total Profit is 21,000 RS.

Case 4:

If the partners invest different amounts for different time periods, then their profit and loss will be shared in the ratio of their equivalent capital or money time capital.

Example:

A, B, and C started a business each investing 25,000 Rs. After 5 months A withdrew 5,000 Rs., B withdrew10,000 Rs. And C invested Rs 5,000 more. Find the share of each if after one year total profit is 16,600 Rs.

Solution:

A invested 25000 for 5 months and after 5 months 5000 Rs was withdrawn. So for the rest of 7 months, his capital was 20000 Rs

B invested 25000 for 5 months and after 5 months 10000 Rs was withdrawn. So for the rest of 7 months, his capital was 15000 Rs

C invested 25000 for 5 months and after 5 months 5000 Rs was invested again. So for the rest of 7 months, his capital was 30000 Rs

The ratio of the money time capital of A, B, C is

(25000 X 5) + (20000 X 7) : (25000 X 5) + (15000 X 7) : (25000 X 5) + (30000 X 7)

= (125000 + 140000) : (125000 + 105000) : (125000 + 210000)