Partnership | Quantitative Aptitude for SSC CGL PDF Download

What is a Partnership?

A partnership refers to a legal arrangement between two or more people to jointly establish and run a business, with profits (and losses) divided among them. Essentially, it's a binding contract where co-owners collaborate to manage an organization, divide operational duties, and split the financial outcomes—whether gains or setbacks—generated by the venture.

In a standard partnership, participants typically share both benefits and risks equally. However, certain structures allow for limited liability, where some partners' exposure to losses is capped. It's also possible for one or more partners to remain hands-off, avoiding involvement in daily operations.

Types of Partnerships

Partners can be categorized by their roles: a "sleeping" (or silent) partner provides only financial backing without participating in management, while a "working" partner invests capital and actively oversees the business. These distinctions lead to two main partnership categories: simple partnerships and compound partnerships.

Simple Partnership

In a simple partnership, all contributors provide resources—such as capital or other assets—for an identical duration. Profits are then distributed proportionally based on each person's input. The formula for calculating shares in a simple partnership is outlined below:

Simple Partnership Formula

If we consider X and Y as two contributors who contribute P and Q amount respectively for a year in a particular business, then their profit or loss earned at that time will be:
X’s profit or loss: Y’s profit or loss = P : Q

Compound Partnership

As the name suggests in such a partnership, the money is funded during distinct periods by numerous investors. Also, the benefit-sharing ratio is confirmed by replicating the capital contributed with the unit of time.

Compound Partnership Formula

The compound partnership formula is as follows:
X1 : X2 = Y1 × Z1 : Y2 × Z2
X1 = 1’st partners’ earnings.
Y1 = 1’st partners investment.
Z1 = time for which 1’st partner contributed his money.
X2 = 2’nd partners earnings.
Y2 = 2’nd partners investment.
Z2 = time for which 2’nd partner contributed his money.

Relation between profit and capital 

Candidates can find the relationship between profit and capital from below.

• Profit (P) ∝ Capital (C)
• P1 : P2 = C1 : C2

Change in Capital

In this type of partnership problem the capital value changes over time.

Rent Distribution

In this type of partnership problem, the rent is distributed in the available people by following a ratio.

Condition Dependent 

In this type of partnership problems, the question consists of some predefined conditions.

How to Solve Question Based on Partnership – Know all Tips and Tricks 

Candidates can find different tips and tricks from below for solving the questions related to partnership.

Tip # 1: Candidates need to make sure that they know all the important formulas of partnership which are mentioned below.

• Profit ∝ investment
• Profit ∝ time
• Profit (P) ∝ Capital (C)
• P1 : P2 = C1 : C2

Tip # 2: The first two formulas shall be applied only when the Time Period is same or constant.

Partnership Solved Sample Questions

Q1: P, Q and R started a business with Rs.10,000, Rs.12,000 and Rs.15,000 respectively for 2 years and they got Rs.55,500 as profit. Find the Q’s share in the profit.
Sol: 
Ratio of investment of P, Q and R = 10,000 : 12,000 : 15,000 = 10 : 12 : 15
The profit of Q = 12 / (10 + 12 + 15) x 55,500 = 12 x 55,500 / 37 = Rs.18,000

Q2: P, Q and R entered into the partnership. P contributes Rs. 14,000 for 5 months, Q contributes Rs. 28,000 for 7 months and R contributes Rs. 21,000 for 4 months. If the total profit made is Rs. 12,500, then find the profit of R.
Sol: 
P1 : P2 : P3 = C1T1 : C2T2 : C3T3
P1 : P2 : P3 = 14,000 × 5 : 28,000 × 7 : 21,000 × 4 = 5 : 14 : 6
The profit of R=6 / (5 + 14 + 6) x 12,500 = 6 x 12,500 / 25= Rs.3000

Q3: P, Q and R started a business respectively with Rs.100000, 120000 and 180000 for one year. After 2 months P adds Rs.20000, Q and R respectively withdraws Rs.40000 and Rs.8000. If at the end of 1 year P gets Rs.400 more than R, then find the total profit.

Sol: 
Ratio of profit of (P : Q : R) = (100000 × 2) + (120000 × 10) : (120000 × 2) + (80000 × 10) : (180000 × 2) + (100000 × 10)
Profit of (P : Q : R) = 140 : 104 : 136 = 35 : 26 : 34
Let the profit of P, Q and R be 35x, 26x and 34x 35x – 34x = 400
x = 400
∴ Total profit = 35x + 26x + 34x = 95x = Rs.38,000

Q4: P, Q and R rented a meadow. P puts 10 cows for 7 months, Q puts 21 cows for 2 months and R puts 14 cows for 6 months. If the rent of the meadow is Rs.3570, how much must R pay (in rupees) as his share of rent?
Sol:
P : Q : R = 10 × 7 : 21 × 2 : 14 × 6
P : Q : R = 5 : 3 : 6
Share of R= 6 / (5 + 3 + 6) x 3570 = 3 x 3570 / 7 = Rs.1530

Q5: P and Q started a business and the ratio of their investment is 5 : 7. They decided that 70% of the profit will be divided into equal parts and the rest of the profit will be divided into the ratio of their investments. If Q got Rs.500 more than P, find the total profit.
Sol: Let the total profit earned be x, According to the question,
2 / 12 x 30x / 100 = 500
x = Rs.10000