# 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.

## What is Business 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.

You May Also Like: **Types of Business Ownership**

### 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**

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