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Partnership Problems and Concepts For CAT Exam

The topic of partnership is an essential part of the CAT quantitative aptitude segment. These questions are repeated almost every year and thus, CAT aspirants are suggested to be properly acquainted with this topic to be able to solve the related questions easily in the exam. A detailed explanation along with solved examples on the topic of partnership is given here to help the individuals learn this topic more efficiently.

What is a Partnership?

A partnership is whenever at least two individuals hold hands with a shared objective to achieve benefits. Each accomplice contributes either time, cash or licenses to enable the association firm to harvest benefits.

A partner who only invests money is called a Sleeping Partner and a partner who invests money and mainly manages the business is called the working partner. Some other important points associated with partnership are given below.

  • Whenever at least two individuals hold hands to make a start-up or some business it’s known as an ‘association’ business.
  • Regularly, they contribute some capital and procure some benefits. Furthermore, this benefit is circulated among accomplices either in some prefixed proportion or the proportion of their venture.
  • When the periods of investment are equal, the profits or losses are in the ratio of the corresponding investments.

These points are better understood by knowing the types of partnerships. The detailed explanations of the different types of partnerships are given below:

Types of Partnerships:

There are mainly two types of partnership i.e. simple and compound partnerships. The details of both of them are given below.

Simple Partnership

In such partnerships, the resources are invested for the same time period by all the investors i.e. the capital (or other resources) stays in the business for the same duration. In this kind of partnership, the profit is distributed in proportion to their contributed resources.

  • Rule 1: Simple Partnership Formula

If P and Q contributed Rs. a and b respectively for one year in a business, their profit (or loss) at that time will be-

=> P’s benefit (or misfortune) : Q’s profit(or misfortune) = a : b

Compound Partnership

In a compound partnership, the money is invested for different periods of time by different investors. In this, the benefit-sharing proportion is ascertained by duplicating the capital contributed with the unit of time (generally months).

  • Rule 2: Compound Partnership Formula

=> P1 : P2 = C1 × T1 : C2 × T2


P1 = Partner 1’s Profit.

C1 = Partner 1’s Capital.

T1 = Time period for which Partner 1 contributed his capital.

P2 = Partner 2’s Profit.

C2 = Partner 2’s Capital.

T2 = Time period for which Partner 2 contributed his capital.

Sample Partnership Problems For CAT

Question 1:

Anmol and Bhuvesh invested Rs.1500 and Rs.2000 respectively in a firm. After 4 months, they admit Suresh who contributed Rs.2250. Bhuvesh withdraws his contribution after 9 months. What would be Bhuvesh’s share if the profit at the end of the year was Rs. 900?


To solve this, it is important to calculate the ratio of their contribution first. It is given that Anmol invested his capital for 12 months while Suresh invested his capital for (12 – 4=) 8 months and Bhuvesh invested for 9 months.

So, Anmol : Bhuvesh : Suresh = 1500 × 12: 2000 × 9: 2250 × 8 = 180 : 180 : 180

=> Anmol : Bhuvesh : Suresh = 1 : 1 : 1.

Now, Bhuvesh’s share will be = {1 / (1 + 1 + 1)} = 1/3rd of profits = (1/3) × 900 = Rs. 300.

Question 2:

Rakesh contributes one-fourth of capital for one-fourth of the time. Raju contributes one-fifth of capital for half of the time and Ramu contributes the remaining capital for the whole time. Calculate their profit-sharing ratio.


Part of Capital by

Rakesh = 1/4 ;

Raju = 1/5 ;

Ramu gave remaining ⇒ Ramu’s share in capital = 1 – (1/4 + 1/5) = 11/20

Time investment by: Rakesh = 1/4; Raju = 1/2; Ramu = 1 (whole time means full one 1 year)

Using, P1: P2 = C1×T1: C2×T2

⇒ A: B : C = 5: 8: 44.

Now we’ll take LCM of 16, 10 and 20 which is 80 and divide it by each denominator and multiply the number thus obtained by each of the respective denominators.

⇒ A: B: C = 5: 8: 44.

Question 3:

X began a business with Rs.450. Then, after a few months, Y joined him with a capital of Rs.300. In the end, the profits were distributed in the ratio of 2:1. After how long did Y join?


Capital by: X = 450, Y = 300

Time capital stay invested by: X = 12, Y = n (say)

Using, P1: P2 = C1×T1: C2×T2

(2/1) = (450×12)/(300n)

⇒ n = 9 months

So, Y’s capital was invested for 9 months and he joined after (12 – 9) = 3 months.

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