# How to Solve Business with Partnership Problems

This post will explain how to solve problems on business with partnership. As partnership problems are more common in every job/recruitment test. Students will explore the formula and method to solve the problem on business with partnership.

When two or more people run a business together, they are referred to as partners, and the transaction is referred to as a partnership.

## Ratio of division of gains

• When all the partners’ investments are for the same period of time, the gain or loss is distributed among them in proportion to their investments.

If A and B each invest Rs. x and Rs. y in a firm for a year, then at the end of the year:

(A’s profit share): (B’s profit share) = x: y

• When investments are for distinct time periods, equivalent capitals for a unit of time are determined by taking (capital x number of units of time).

Now, the gain or loss is split by the capitals’ ratio. 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.

### Working and sleeping partners

A working partner is one who operates the firm, whereas a sleeping partner is one who only invests money.

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### Example Problems on Business with Partnership

Problem 1

In a 5:3 ratio, A and B invest in a business. If 4% of the total profit is donated to charity and A’s portion is \$850, what would be the total profit?

Solution:

Let the total profit be \$100.

5% of total profit goes to charity. So 4% x 100 = 4.

Now \$4 will be deducted from \$100, So, 100-4 = 96

Our new total profit remains = \$96.

 After paying to charity, A’s share = Rs. 96 x 5 = \$60. 8

If A’s share is \$60, total profit = \$100.

 If A’s Share \$850, total profit =  \$ 850 x 100 = \$1416.16. 60

Problem 2

A, B, and C discussed the possibility of starting a business together. A committed to invest \$6500 for six months, \$8400 for five months, and \$10,000 for three months. A want to be a working member, for which he will be paid 5% of the profits. A profit of \$7400 was made. Calculate B’s profit contribution.

Solution:

As per question, A wants to be the working member for which, he was to receive 5% of the profits. So,

We have been given total profit i.e. \$7400

A will get 5% of the total profit, so 5% of 7400 = \$370

Here, \$7400 – \$370 = \$7030

Now Total profit is  \$7030

Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)

= 39000 : 42000 : 30000

= 13 : 14 : 10

Now on the basis of ratio, we calculate share of B

B= \$7030 x 14 = \$2660. 37

### 4 Responses

1. April 21, 2022

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