## Partnership Problems

__(Quantitative Reasoning)__

There are two kinds of partnership:

⑴ Simple Partnership

⑵ Compound Partnership

⑴ Simple Partnership

In this partnership, time remains the same in case of each partner.

Suppose A and B are two partners. A invests ₹p and B invests ₹q then,

*Share of Partner A's profit/loss : Share of Partner's B profit/loss = p : q*

⑵ Compound Partnership

In this case, time is different.

Suppose A and B are two partners. A invests ₹p for m months and B invests ₹q for n months then,

*Share of Partner A's profit/loss : Share of Partner's B profit/loss = p×m : q×n*

__Important points to remember:__

1. Profits of given number of partners is divided in the ratio of their capitals considering the time periods for which the respective capitals remain in the business.

2. When the time periods are different, the capitals are reduced to a unit (e.g. month) by multipling the capital to number of months for the given duration.

__Problems and Solutions__

**Q1: A and B started a business with capitals of Rs. 2500 and Rs. 6000 respectively. Find the share of A and B out of an annual profit of Rs. 1600.**

Answer: Ratio of shares of A and B = Ratio of their investments = 2500 : 6000 = 5 : 12

A’s share = (5/17) × ₹1600 = ₹470.58

B's share = (12/17) × ₹1600 = ₹1129.42

**Q2: A, B and C rent a house together for 2 years at ₹360 p.a. After 5 months C left the house. After 8 months more, B also left. How much rent should ech pay?**

Answer: Time = 2 years = 24 months

Rent for 5 months = (360 × 2 × 5) /24 = ₹150

Rent for C = 150/3 = ₹50

Rent for 8 months = (360 × 2 × 8) /24 = ₹240

Share of B = 240/2 = ₹120

Total Rent by B = 120 + 50 = ₹170

Rent of A = 720 - (Rent of B + C)

= 720 - (170 + 50)

= ₹500