# Partnership Problems with Shortcut Methods - Introduction

Hi friends, I am Aindree. An SBI PO aspirant. Here I am going to share Aptitude notes which I have been using for my preparation. I hope this will be helpful for my fellow aspirants. Happy Reading :)

### Partnership Introduction

When two or more persons start a business jointly and share the profit or loss threof in an agreed proper portion, it is known as partnership business and the persons carrying on such business are called Partners. Generally partners share the profit or loss in the ratio of the capitals invested by them. Partnership may be of two types. They are,
Let's have a detailed look about these types of Partnerships.

Simple Partnership : When the capitals of the partners are invested for the same time, then this type of partnership is called simple partnership. In such a case, the profit or loss is distributed in proportional to the capital invested.

Compound Partnership : When the capital, which is equal or unequal, of the partners, is invested for different times, this type of partnership is called compound partnership. In such a case the profit or loss is distributed in proportional to the products of the capital and the periods of their investment.

An Important formal for Solving the Problems of Partnership is

(Capital of A x time invested in capital of A) / (Capital of B x time invested by Capital of B) = Profit of A / Profit of B

Working Rule -
1. If the ratio of investment by three persons is a : b : c and ratio of time invested in their capital is x : y : z then the ratio of their profit will be ax : by : cz.
2. If the ratio of investment by three persons is a : b : c and ratio of their profit is p : q : r then, the ratio of time invested in their capital will be p/a : q/b : r/c
Now let's have a look at some examples.

Example 1 : A, B and C enter into partnership. A contributes one-third of the capital while B contributes as much as A and C together contribute. If the profit at the end of the year amounts to Rs. 840 what would each receive ?

Solution :

As A contributes one-third of the capital

=> A's profit = 840/3  =Rs. 280

Now as B contributes as much as A and C

So profit of B = Profit of A + Profit of C =  Rs. 280 + Profit of C

=> Profit of B - Profit of C = Rs. 280

and Profit of B + Profit of C = Rs. 840 - Rs. 280

adding 2 Profit of B = Rs. 840

Profit of B = Rs. 420

Hence profit of C = 840 - 420 - 280

= Rs. 140

Example 2 : A is working and B is sleeping partner in a business. A puts Rs. 5,000 and B puts in Rs. 6,000. A receives 12 1/2% of the profit for Managing the business and the rest is divided in proportion of their capitals. What does each get out of a profit of Rs. 880 ?

Solution :

The amount, which A receives for managing the business = 12 1/2 % of Rs. 880

= (25 / (2 x 100)) x 880 = Rs. 110

The amount left = 880 - 110 = Rs. 770

The amount left is to be divided in the ratio = 5,000 : 6,000 = 5:6

Out of the amount left, A's share  =  (5/11) x 770 = Rs. 350

Out of the amount left, B's share = (6/11) x 770 = Rs. 420

Total share received by A = 110 + 350 = Rs. 460

Share received by B = Rs. 420

Example 3 : A and B enter into a partnership. A contributes Rs. 5000 while B contributes Rs. 4000. After 1 month B withdrawn 1/4 part of his contribution and after 3 months from the starting A puts Rs. 2000 more. When B withdraws his money at the same C also joins them with Rs. 7000. If at the end of 1 year there is a profit of Rs. 1218, what will be share of C in the profit ?

Solution :

Since the contribution of three partners are different and their times also differ. Therefore, their contributions should be converted for equal durations. For this, contribution is multiplied by time.

=> Contribution of A = Rs, 5000 for 12 months + Rs. 2000 for 9 months

Contribution of A for 1 month = 5000 x 12 + 2000 x 9

= 60000 + 18000 = Rs. 78000

Contribution of B = Rs. 4000 for 1 month + 3/4 of Rs. 4000 ofr 11 months

=> Contribution of B for one month = 4000 x 1 + 3000 x 11

= 4000 + 33000 = Rs. 37000

=> Contribution of C = Rs. 7000 for 11 months

Contribution of C for 1 month = 7000 x 11 = Rs. 77000

=> Ratio in their contributions = 78000 : 37000 : 77000

= 78 : 37 : 77

=> Sum of their ratios = 78 + 37 + 77  = 192

=> Share of C in the profit  = (77 x 1218) / 192  = Rs. 488.47

Example 4 : Alok started a business by investment of Rs. 90000 after 3 months Pranav joned him with an investment of Rs. 120000. If they had a profit of Rs. 96000 after 2 years then what is the difference in the shares of two ?

Solution :

Alok's investment for 1 month = 90000 x 24 = 2160000

Pranav's investment for 1 month = 120000 x 21 = 252000

=> Ratio of their investment =  6:7

=> Required difference  = ((7-6) x 96000) / (6+7)

= Rs. 7384

Example 5 : A, B and C started a business in partnership. A invested Rs. 25 lacks and after 1 year he invested Rs. 10 lacks more. B invested Rs. 35 lacks in the beginning and withdrew Rs. 10 lacks after 2 years. C invested Rs. 30 lacks. What is the ratio of their profit after 3 years ?

Solution :

A's investment = 25 x 3 + 10 x 2  = Rs. 95 lacks

B's investment = 35 x 2 + 25 x 1  = Rs. 95 lacks

C's investment = 30 x 3  = Rs. 90 lacks

Ratio of their investment = 19 : 19 : 18

Ratio of their profit = 19: 19 : 18

(because time period is same, i.e., for 3 years)

That's all for today friends. In my next lesson I will try to cover more examples higher difficulty level along with examples. All the Best :)

shared by Aindree Mukherjee