Quant (Concepts): Partnership

Quant (Concepts): Partnership

When a business is completely owned by a single person it is called single ownership, whereas, when two or more people together own a business it is called partnership and those people are called partners. The money contributed by these people is called their investment.

Does partnership always result in profit?

The answer is No. Since every business has ups and downs, profit or loss, so does the share of return for partners. The Profit or loss that a business incurs is shared by the partners in the ratio of their total investments, where,

Total investment = (investment × number of units of time)

For example: If A invests Rs 1000 for 5 months and B invests Rs 3000 for 2 months then the ratio of their total investments = (5 × 1000) : (2 × 3000) = 5 : 6.

Note:

For calculating the ratio of total investments,you need to multiply number of units of time only when this time period is different for the partners. If the time period is same, it will ultimately be cancelled out.

Example 1:

There are 3 partners A, B, C who invest Rs 40000, Rs 48000, and Rs 56000, respectively in a business, which incurs a total loss of Rs 36000.

How much loss will each partner bear?

Solution:

The ratio of total investments of  A, B, C = (40000:48000:56000) ⇒ 5 : 6 : 7

Loss incurred by A = Rs. 5/18 × 36000 = Rs 10000

Loss incurred by B = Rs. 6/18 × 36000= Rs 12000

Loss incurred by C = Rs. 7/18 × 36000= Rs 14000

Example 2:

A started a business by investing Rs 45000. After 3 months, B joined him with a capital of Rs 60000. After another 6 months, C joined them with a capital of Rs 90000. At the end of the year, they made a profit of Rs 20000. After calculating this profit, they came across an expense of Rs 40000, which is yet to be paid.

What is the profit or loss that each partner will incur?

Solution:

A’s investment of Rs 45000 is for full year, B‘s investment ofRs 60000 is for 9 months and C’s investment of Rs 90000 is for 3 months.

The ratio of the total investments of A, B and C = (45000 × 12) : (60000 × 9) : (90000 × 3)

⇒ 2 : 2 : 1.

At the end of year, total profit earned was Rs 20000 but an expense of Rs 40000 was to be paid. Hence there was a net loss of Rs. 20000.

Since profit and expense both are to be shared by the partners in the ratio of their total investments.

Loss incurred by A = Rs. 2/5 × 20000 = Rs. 8000

Loss incurred by B = Rs. 2/5 × 20000= Rs. 8000

Loss incurred by C = Rs. 1/5× 20000= Rs. 4000

Example 3:

A, B and C went fora picnic. A carries 7 breads with him and B carries 8 breads with him, whereas C carries nothing. They shared the breads equally. C paid Rs. 30 as his share.

How much amount out of this should be paid to B?

Solution:

As they shared the breads equally, they would have eaten 15/3 = 5 breads each. C pays Rs. 30 as his share for 5 breads. It implies that the cost of one bread is 30/5 = Rs. 6.

As out of the 8 breads that B carries, he himself eats 5, thus, he gave 3 breads to C. For that, he should be paid 3 × 6 = Rs. 18.