# Partnerships

Partnership is closely related to Ratios. A student must be thorough in his understanding of ratios before doing sums on partnership.

**BASIC CONCEPTS:**

(i) When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership.â€¨

(ii) When investment of all the partners are for the same time, the profits or losses are divided among them in the ratio of their investments.

(iii) When investments are for different times, then equivalent capitals are calculated for a unit of time by multiplying the capital with the number of units. Gains or losses are divided in the ratio of these capitals.

(iv) A partner who manages the business is called a working partner while the one who simply invests money but does not look after the business is called a sleeping partner.

# Concept 1: Distributing Profits

**â–º**** If the business is started by all the partners at the same point of time then the profit is distributed in the ratio of their capitals, or in other words if the capitals of the partners remain in the business for the same duration of time then the profit in simply distributed in the ratio of their capitals.**

**Illustration 1:**

Three partners A, B, C invest Rs. 26000, Rs. 34000 and Rs. 10000 respectively in a business. Out of a profit of Rs. 3500, what is B's share?

Bâ€™s share will be = B/Total Investment Ã— Total profit = 34000/70000 Ã— 3500 = 1700.

**When equality is given, equate all the terms to x.**

**Illustration 2:**

If 6 (A's capital) = 8 (B's capital) = 10 (C's capital), then what is the ratio of their capital?

The tendency is to tick the easiest choice, which is 6 : 8 : 10, but it is wrong.â€¨

We have to equate all the terms to x, hence 6A = 8B = 10C = x. Then A = x/6, B = x/8 and C = x/10. Ratio of A : B : C is x/6 : x/8 : x/10.

Taking the LCM of the denominators, we get A = 20x, B = 15x and C = 12x. Hence the ratio of their capitals is 20 : 15 : 12.

# Concept 2: When Partners Join at Different Times

**â–º**** If the different partners join at different points of time then their profit sharing ratio is calculated by multiplying the capital invested with the number of months the capital remains in the business.**

**Illustration 3:**

Sanjay and Raj started a business and invested Rs. 20,000 and Rs 25,000 respectively. After 4 months, Raj left and Naresh joined by investing Rs 15,000. At the end of the year, there was a profit of Rs 4,600. What is the share of Naresh?

Sanjay stays for 12 months, so his share is 20 Ã— 12 = 240. Raj stays for 4 months, so his share is 25 Ã— 4 = 100. Naresh joins after 4 months, so he stays for 8 months = 15 Ã— 8 = 120. The ratio of sharing is thus 240 : 100 : 120. Hence Nâ€™s share = 120/460 Ã— 4600 = 1200.

**Illustration 4**:

A, B and C went to a picnic with A having 7 breads with him, B having 5 breads and C contributing Rs. 40 as his share. They shared the breads equally. How much should be given to A out of the amount brought by C?

There are 12 breads, which have been shared equally. Now C has taken 4 breads from them and has paid Rs. 40 for that. This means the cost of one bread is Rs. 10. Because he took 3 breads from A and 1 bread from B (A and B ate 4 breads themselves) therefore he will pay Rs. 30 to A and Rs. 10 to B.