# What is Partnership and How to solve Partnership Questions?

In this post, we will discuss What is Partnership and Solve Partnership Questions using Formulas to save time in Bank Exams

Partnership Questions are one of the most important questions that appear in Bank Exams. Partnership Questions are based on the concept of ratio and proportion. Often partnership questions ask you to find the share of profit of individuals. These questions are logic based questions which can be easily solved with the help of formulas. If you understand the term partnership then, you can easily solve partnership questions by just using formulas.

In this post, we will discuss, What is Partnership? Formulas to solve partnership Questions and few solved examples using partnership formulas to save time in Bank Exams.

What is Partnership?
A partnership is a type of business organisation where two or more individuals come together – Pool money, skills, resources, share profit and losses.

For example: A and B started a business with an investment of Rs.1,00,000 each. This means that A and B are 50% partners and they share their profit and loss equally.

Formulas to solve Partnership Questions
Partnership questions generally ask you to find the profit share of the different people.

Let us assume there are two people A and B and they have come together to run a business. To start a business they need to invest. So, both of them invest 1.5 lakh each. At the end of the year when profits are divided among them, they are divided equally because a person's profit is directly proportional to the investment and profit is directly proportional to the time period.
Hence, Profit is directly proportional to the product of Investment and Time Period.
To find the ratio of profit shares,
If there are three partners, then the ratio of their shares of profit will be denoted as
Example 1: Partnership Questions

Question: Meena started a business investing Rs 12000. After 5 months, Abhay joined her with a capital of Rs.9000. At the end of the year, the total profit was Rs.4416. What is the share of profit of Meena?
Solution:
Step 1:
Investment of Meena = I= Rs.12000
Time period = T1 year i.e. 12 months
Investment of Abhay = I= Rs.9000
Time Period = T12 – 5 = 7 (Since he joined 5 months late)
Total Profit = Rs.4416

Step 2:
To find the ratio of share of profits of Meena and Abhay, we use the formula
PM : PA = IM x TM : IA x TA

Step 2:
By substituting the values  in the formulas
12000 x 12/ 9000 x 7
= 16/7

Step 3:
From the ratio, we find Meena's share of profit
PM = 16/(16 + 7) x 4416
= 3072

Therefore, Meena's share of profit is Rs.3072.

Example 2: Partnership Questions

Question: Pankaj and Nitin started a business by investing Rs.4200 and Rs.5700 respectively, but Nitin left the business after 8 months. Find the difference between the share of profits of Pankaj and Nitin, if the total profit at the end of the year was Rs.26000.

Solution:
Step 1:
Investment of Pankaj = Ip = Rs. 4200
Time period = T= 1  year i.e. 12 months
Investment of Nitin = IN= Rs.5700
Time Period = TN = 8 months
Total Profit = Rs.2600

Step 2:
Formula
PP : PN= Ip x Tp : IN x TN

Step 3:
By substituting the values in the formula
PP: PN = 42000 x 12 : 57000 x 8
PP: PN = 42 x 12 : 57 x 8
PP: PN = 21 : 19

Step 4:
To calculate the difference between the share of profit we take the difference in their ratios with the total ratio and multiply it with the total profit.
21 - 19 = 2 (Difference in the ratio)
21 + 19 = 40 (Total ratio)

Step 5:
2/ 40 x 26000 = 1300

Therefore, the difference between their shares of profit is Rs.1300.
Example 3: Partnership Questions

Question: Sarita started a business investing Rs.50000. After 6 months, Abhishek joined her with Rs.75000. After another 6 months, Nisha also joined them with Rs. 1.25 lakh. What should be the ratio in which the profit is shared by the 3 people respectively at the end of 2 years?

Solution:
Step 1:
Investment of Sarita = IS = Rs.50000
Time period =TS 24 months
Investment of Abhishek =IA Rs.75000
Time period = T18 months
Investment of Nisha =IN = Rs.1.25 lakh
Time period = TN = 12 months

Step 2:

PS:PA:PN =  IS x TS : IA x TA : IN x TN

Step 3:
PS:PA:PN = (50,000 x 24) : (75000 x 18) :  (125000 x 12)

Step 4:
By simplification,
8: 9: 10

Therefore, 8: 9: 10 is the ratio in which profit is shared between Sarita, Abhishek and Nisha respectively at the end of 2 years.

Example 4: Partnership Questions

Question: Subash started a business by investing Rs.25000. 6 months later Aditya joined him by investing Rs.15000. After another 6 months, Aditya invested an additional amount of Rs15,0000. At the end of 3 years, they earned a profit of Rs.2,47,000. What is Aditya's share?

Step 1:
Investment of Subhash =IS 25000
Time period = Tyears
Investment of Aditya =IA1 = 15000
Time period = TA1 30 months
Investment of Aditya = IA2 15000
Time period = TA2 24 months

Step 2:
PS : PA = IS x TS : [ (IA1 x TA1) +  IA2 x TA2]

Step 3:
S : A = (25000 x 36) : (15000 x 30 + 15000 x 24)
= 30: 27
= 10: 9

Step 4:
Aditya’s share = 9/19 x 2,47,000 = 1,17,000

Therefore, Aditya’s share of Profit at the end of 3 years = 1,17,000

Practice Partnership Questions for Bank Exams

Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda Joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran’s share in the profit?
1) Rs.9423       2)10,500        3) 12,500       4)14,000      5) None of these
Question: Aman started a business investing Rs. 70,000 Rakhi Joined him after six months with an amount of Rs. 1,05,000 and Sagar Joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
1) 7: 6:10      2) 12:15:16      3)42:45:56    4) Cannot be determined    4) None of these