Partnership : Definition, Concepts, Types of Partnership

Partnership is an easy and scoring topic in Quantitative Aptitude. In this article, we cover formulae of partnership, concept and the type of questions asked in exams. It covers 1 to 2 questions in the preliminary exam and covers 3 to 4 questions in the main exam. After reading this article candidates have no doubts about the topic.

Definition & Concept of Partnership

When two or more individuals involved in a business or an agreement invest some money to run the business. Individuals who invest money are called partners. 

Types of Partner

There are two types of Partners: 

1. Active Partner:

The partner who actively manages the business voluntarily is known as an Active Partner.

2. Sleeping Partner:

The partner who only invests money in the business but does not manage the business voluntarily is known as Sleeping Partner.

Types of Partnership

There are two types of Partnership:

1. Single Partnership:

It is the partnership in which only a single individual can run a business is called a Single Partnership.

2. Compound Partnership:

It is the partnership in which two or more individuals invest in a business and run it is called a Compound Partnership.

Formula for Partnership:

Profit = investment × time 

If P1, P2, and P3 are profits of three persons and their investments are x:y:z respectively. t1 : t2 : t3 is the ratio of time of their investments.

Case1:- if the ratio of profit and investment is given, we have to find the ratio of time 

t1 : t2 : t3 = P1/x : P2/y : P3/z 

Case2:- when we have to find the ratio of investments 

x : y : z = P1/t1 : P2/t2 : P3/t3 

Important Questions on Partnership

Q1. Three partners P, Q and R invested in a business. P invested 5000 for 7 months, Q invested 6000 for 5 months and R invested 7000 for 3 months. Find the ratio of their profits.

a) 30:35:21 

b) 35:30:21 

c) 7:5:3 

d) none of these 

e) All are correct.

Solution:- Profit = investment × time

P:Q:R = 5000×7 : 6000×5 : 7000×3

P:Q:R = 35:30:21

Hence option b) is correct.

Q2. P, Q and R started a business by investing 50000, 60000 and 70000 respectively. P is a working partner and gets 20% of the profit as an extra allowance and the remaining profit is distributed in their ratio of investments. If the profit received by R is 28000, then find the total profit.

a) 90000 

b) 72000 

c) 81000 

d) 86400 

e) none of these

Solution:- let, total profit = x 

Ratio of investments:- P:Q:R = 5:6:7

x × 4/5 × 7/18 = 28000

x = 90000 

Hence option a) is correct.

Q3. Rs20000 was invested by Aman and Anurag in a business. They got a total profit of Rs 3000 at the end of the year. Aman got Rs 1800 as a share of the profit. How much amount did Anurag invest? 

a) 10000 

b) 9000 

c) 12000 

d) none of these 

e) 8000

Solution:- 

the ratio of profit,

Aman:Anurag = 1800:1200 = 3:2

Amount invested by Anurag:- 20000×2/5 = Rs 8000

Hence option e) is correct. 

Q4. A and B enter into a partnership with an investment of 4:7. After 6 months A adds 25% of the investment and B adds 14.28% of the investment. If the annual profit is Rs 9.6 lakhs, find the share( in lakhs) of A.

a) 3.6 

b) 6 

c) 2.4 

d) 4.8 

e) none of these

Solution:- Ratio of investments:- A:B = 4×6+5×6 : 7×6+8×6 = 54:90 = 3:5

Profit of A:- 9.6×3/8 = 3.6 lakhs 

Hence option a) is correct. 

Q5. P,Q and R started a business. P’s investment is four times the investment of Q and Q’s investment is three times the investment of R. If the yearly profit after a year is ₹14.4 lakhs. Find the difference in investment (in lakhs) of Q and R.

a) 2.4 

b) 2.2 

c) 2 

d) 1.8 

e) none of these 

Solution:- P = 4Q ⇒P:Q = 4:1 

Q = 3R ⇒Q:R = 3:1 

Combined ratio of investment:- 12:3:1 = 16 units

Total profit:- 14.4 lakhs 

Investment of Q:- 14.4×3/16 = 2.7 lakhs 

Investment of R:- 14.4×1/16 = 0.9 lakhs 

Required Difference:- 2.7 – 0.9 = 1.8 lakhs 

Hence option d) is correct. 

Q6. A, C and D started a business in the ratio of investment 1:4:3. After every 3 months, A doubles his investment, C halves his investment and D’s investment remains unchanged. If the share of profit of D is ₹50,000. Find the total profit. 

a) 143750 

b) 134250 

c) none of these 

d) 125000 

e) 145350 

Solution:- A:C:D = 1:4:3 

After every 3 months ratio of investment:- 

1×3+2×3+4×3+8×3 : 4×3+2×3+1×3+0.5×3 : 3×12 

A:C:D = 5 : 2.5 : 4 

Total Profit:- 50000×11.5/4 = ₹143750 

Hence option a) is correct. 

Q7. X starts a business with some investment. After 4 months, Y joins the business and after another 2 months, Z joins the business. At the end of the year, the ratio of their profit is 3:4:6. Find the ratio of their investment. 

a) 2:1:4 

b) 4:1:2 

c) 1:2:4 

d) none of this 

d) can’t be determined 

Solution:- Profit = investment × time 

3:4:6 = (x:y:z) × (12:8:6) 

3:4:6 = (x:y:z) × (6:4:3) 

x:y:z = 3/6 : 4/4: 6/3 

x:y:z = 1/2 : 1: 2 

x:y:z = 1:2:4 

Hence option c) is correct.