Partnership: Concept & Tricks

Let us imagine 2 people Alma and Balma who start a business amongst themselves sharing an equal amount of capital. They will get the same amount of profits/loss. But what would happen if they enter different amounts or they invest for different periods of time or even worse, they invest different amounts for the different time duration.
Before solving Partnerships Questions, let us discuss two types of the partnership:
Simple Partnership:
Unequal investment & equal time Period: Considering two people discussed above Alma & Balma started a business with Rs. 1 lakh & 100 each. So at the end of the year, if there is the profit of Rs. 10000 who do you think will get more share in this profit. Of course, the one with 1Lakh investment because he had taken more risk in the business venture (the exact amount of their profit we will discuss).
So, Profit ∝ investment (Time Period constant) 
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Equal Investment & unequal time period: Consider a scenario where Alma & Balma Just had Rs. 100 each on them but Alma Invest for 10 years & Balma invest for 1 year. And after 10 years their business gives them a profit of Rs. 1Lakh.As Alma had invested for a longer duration, he would get more shares in the profit.
So, Profit ∝ Time (Investment constant) 
Compound partnership:
If the time and investment both begin change according to the requirements of the investors, we simply need to combine the above stated equations into one. The result obtained will be:
Profit ∝   investment × time
Also, we can also say that ratio of their profits is equal to the ratio of product of their Investment & Time period.
To solve with simple Partnership Problems. Let’s take an example of Math’s Partnership as given as below:
Let us consider Alma invest Rs. 1000 for 2 year & Balma Invest Rs. 2000 for 3 years. At the end profit is Rs. 8000. What is the net profit of Alma & Balma?
Solution:  Profit ∝   investment × time
1000×2: 2000×3= 1:3 => Ratio of their profit = 1:3
Alma’s Profit share= 1 / 4 x 8000 = Rs. 2000
Balma’s Profit share = 3 / 4 x 8000 = Rs. 6000
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Sleeping Partner:
Sleeping Partner gives money, credit or different resources, for example, a land, building or machinery; however, has nothing to do with the business management.
Working Partner:
A partner who has responsibilities for maintaining the business as an active partner. Each partner plays an important role, like production or marketing. Working Partner also gets its incentive due to its management. Then remaining profit is dividing between both according to their investment.
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