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Reading Time: 6 minutes Questions on the concept of partnership keep appearing in different banking exams and IBPS PO Prelims is no exception. The concept is pretty simple. Two or more persons start a business. Their quantum of capital, the point in time when they entered/left the business and their profit sharing ratio are generally the parameters on the basis on which these questions are solved. The profit-sharing ratio is the product of “their capital” and the “duration for which their capital remain employed”.

If C denotes capital, D denotes time and R denotes profit sharing ratio then the following formula comes into the picture:

C1 * D1 : C2 * D2 :: R1 : R2 If only the questions were this easy so as to be based on this formula! Questions asked in the exam nowadays have one or more other concepts mixed. Not only these kinds of questions test multiple concepts it also checks which aspirants are able to handle pressure in the shortest minimum time. Let’s have a look at a question asked in a previous year paper.

## Example 1

A and B started a business with Rs 600 and Rs 500 respectively. After 4 months, C replaces B with X% of B’s capital. After 1 year C’s share out of the total profit 24000 is 5600. Find the value of X.

(a) 60

(b) 70

(c) 75

(d) 66

(e) 65

### Solution

Since A, B and C were involved in business, their profit sharing ratio will be:

600*12 : 500*4 : (500*x/100)*8

Which can be simplified to 180 : 50 : x

So C’s share is x/(230+x) multiplying which with 24000 will give 5600.

24000*x/(230+x) = 5600

Solving this will get you the value of x as 70.

So option (b) is correct.

Standalone partnership questions are generally easy and are rarely asked. These questions are combined with one or more concepts to make the question look difficult. The more practice you do, the more comfortable you will be with different types of questions. You can encounter new types of questions in sectional and mock tests. Take the first mock test free of cost!

## Example 2

P and Q together started a business such that the ratio of investments and ratio of time of investment is 2: 3 and 7: 4, respectively. Find the profit of P out of a total of Rs. 3250.

a) Rs. 1850

b) Rs. 1650

c) Rs. 1800

d) Rs. 1720

e) None of these

### Solution

Ratio of profit share of P: Q = (2 × 7): (3 × 4) = 14: 12 = 7: 6

Therefore, profit share of P = (7/13) × 3250 = Rs. 1750

Hence, option e

## Example 3

Quantity I: Ram and Shyam started a business together with an initial investment of Rs. 30000 and Rs. 25000. After 6 months, Ram withdrew 15% of his initial investment, Shyam added 10% of his initial investment, and Rohan joined them with an investment of Rs. 5000 more than average of the initial investment of Ram and Shyam took together. Find the share of Ram after 2 years out of the total profit of Rs. 62300.

Quantity II: Shruti and Mihika entered into a partnership. Shruti invested Rs. 3000 and Mihika invested 20% more than Shruti. Raj entered after 3 months with 25% more than Mihika. After another 3 months, Raj and Shruti doubled their amount and Mihika increased her amount by 20%. Find the share of Shruti after a year if the total profit was Rs. 4225.5. a)    Quantity-I > Quantity-II

b)    Quantity-I < Quantity-II

c)    Quantity-I ≤ Quantity-II

d)    Quantity-I = Quantity-II or No relation

e)    Quantity-I ≥ Quantity-II

### Solution:

Quantity I: Investment of Ram for first 6 months = Rs. 30000

Investment of Ram for the last 18 months = 0.85 × 30000 = Rs. 25500

Investment of Shyam for first 6 months = Rs. 25000

Investment of Shyam for the last 18 months = 1.1 × 25000 = Rs. 27500 Investment of Rohan for 18 months = (30000 + 25000)/2 + 5000 = Rs. 32500

Ratio of profit share of Ram: Shyam: Rohan = (30000 × 6 + 25500 × 18): (25000 × 6 + 27500 × 18): (32500 × 18)

= 639000: 645000: 585000

= 213: 215: 195

So, profit share of Ram = (213/623) × 62300 = Rs. 21300

Quantity II: Initial investment of Mihika = 1.2 × 3000 = Rs. 3600

Initial investment of Raj = 3600 × 1.25 = Rs. 4500

Ratio of profit share of Shruti: Mihika: Raj = (3000 × 6 + 6000 × 6): (3600 × 6 + 3600 × 1.2 × 6): (4500 × 3 + 9000 × 6)

= 54000: 47520: 67500

= 2700: 2376: 3375

Required share of Shruti = (2700/8451) × 4225.5 = Rs. 1350

Hence, option a.

Hope this article has helped you in understanding the concept of partnership. Take a Free Mock Test of IBPS PO Prelims and see how well do you perform in these kinds of questions.

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