Aptitude Partnership in Maths

The definition of aptitude partnership: In business, a partnership is an association which involves two or more people managing a company together and sharing the profits at an agreed-upon percentage or ratio. The two or more people involved in running the business are the partners.

Sums related to partnerships are significant for any aptitude exam. These sums carry high weightage in the aptitude exams. Let us learn more about the definition of aptitude partnership and the formula of partnership. Further, we will also learn some quick methods to solve partnership sums in Aptitude exams.

What is the formula of partnership?

• Case 1: When all the partners involved in a business association invest for the same time period, the gain or loss received from the investment is distributed among all the partners in the same ratio they invested.

Suppose in a business association, L and M are two partners. Both L and M invest Rs. J and Rs. K respectively for a time period of one year. At the end of 

one year –

                     (L’s share of profit): (M’s share of profit) = J: K.

• Case 2: When all the partners involved in a business association invest for the different time periods, the equivalent capital for unit time is calculated.

Equivalent Capital = Capital invested x Number of units of time

The gain or loss received from the investment is distributed among all the partners in the ratio of the equivalent capital.

Suppose in a business association, L and M are two partners. Both L and M invest Rs. J and Rs. K respectively for a time period of s months and t months, respectively. In the end –

                       (L’s share of profit): (M’s share of profit) = Js: Kt.

Some important terms related to partnership

• The definition of aptitude partnership: In business, a Partnership is an association which involves two or more people managing a company together and sharing the profits at an agreed-upon percentage or ratio.

• Sleeping partner: In a business, a partner who does not involve or takes care of the business after investing is called a Sleeping Partner.

• Working partner: In a business, a partner who actively gets involved or takes care of managing the business after investing is called a Working or Active Partner.

Types of Partnerships

Simple and compound partnerships are the two basic types of partnerships. Both types of partnerships are outlined below.

Simple Partnership

The partnership in which the partners who are running the business invest the total capital at once and for the same period of time is called a Simple Partnership. This means the resources involved or the capital remains in the business for the same time period. The gain or loss received from the investment is distributed among all the partners in the same ratio they invested.

Formula –

Suppose in a business association, L and M are two partners. Both L and M invest Rs. J and Rs. K respectively for a time period of one year. At the end of one year –

                     (L’s share of profit): (M’s share of profit) = J: K.

Compound Partnership

The partnership in which the partners running the business do not invest the total capital at once but rather invest in slots and for different periods of time is called a Compound Partnership. The benefit-sharing proportion can be determined by multiplying the capital contributed by the unit of time (normally months).

Formula –

Suppose in a business association, L and M are two partners. Both L and M invest Rs. J and Rs. K respectively for a time period of s months and t months, respectively.

ProfitL: ProfitM = CapitalL × TimeL: CapitalM × TimeM

                          = Js: Kt

ProfitL = Profit of Partner L

CapitalL= Capital of partner L

TimeL = The Time period for which Partner L contributed the capital.

ProfitM = Profit of Partner M

CapitalM= Capital of partner M

TimeM = The Time period for which Partner M contributed the capital.

Quick Methods to Solve Partnership Sums

• In a business, if two partners invest Rs J and Rs. K for the same time period and the gain earned is Rs G, the share of gain of both of them is given by –  

Rs. J GJ + K and Rs K GJ + K

• In a business, if three partners invest Rs J, Rs. K and Rs. L for the same time period and the gain earned is Rs G, the share of gain of all of them is given by –  

Rs J GJ + K + L , Rs K GJ + K + L ,Rs L GJ + K + L  

• In a business, if two partners invest Rs J and Rs. K for different periods r and s respectively, and the total gain earned is Rs G, the share of gain of both of them is given by –  

RsJ G rJr + Ks and Rs K G sJr + Ks 

• In a business, if three partners invest Rs J, Rs. K and Rs. L for different time periods r, s and t respectively, and the total gain earned is Rs G, the share of gain of all of them is given by –  

RsJ G rJr + Ks + Lt, RsK G sJr + Ks + Lt and Rs L G tJr + Ks + Lt

• In a business, if three partners invest in the ratio J: K: L and the total gain earned is in ratio G1: G2: G3, the ratio of time periods is given by –  

T1:T2:T3 = G1J G2KG3L

Conclusion

In this article, we learned the definition of aptitude partnership and how to solve a partnership ratio. We learned about types of partnerships and some quick ways to solve partnership problems.