Partnership and Share Concept — Formula, Tricks and Solved Examples

Q1. What is partnership in mathematics?

Partnership is a business arrangement where two or more persons invest money jointly in the same business. These persons are called partners. The profit or loss earned from the business is shared among all partners in the ratio of their investments. Partnership is a core topic in business mathematics and is asked in every competitive exam including CAT, SSC CGL, Bank PO and Railway RRB.

Q2. How is profit shared when partners invest for different time periods?

When partners invest for different time periods profit is shared in the ratio of Capital multiplied by Time for each partner. For example if A invests Rs. 14000 for 6 months and B invests Rs. 21000 for 4 months then profit ratio = 14000×6 : 21000×4 = 84000 : 84000 = 1:1. This is called compound partnership and the same rule can be extended for more than two partners.

Q3. How is profit shared when time is not mentioned in partnership?

When time is not mentioned in a partnership problem we assume that all partners have invested for the same time period. In this case profit is shared simply in the ratio of their capital investments. For example if A invests Rs. 45000 and B invests Rs. 63000 then profit ratio = 45000:63000 = 5:7 and total profit is divided accordingly.

Q4. What is a sleeping partner?

A sleeping partner is a type of partner who only puts money into the business but does not actively participate in running or managing it. A sleeping partner receives profit only in the ratio of money invested. Since they do not manage the business they do not get any extra share of profit beyond their investment ratio.

Q5. What is an active partner and how is their profit calculated?

An active partner is a type of partner who not only puts money into the business but also actively runs and manages it. Because of this additional work the active partner gets extra profit as per the agreed conditions. After deducting the active partner’s extra share the remaining profit is then divided among all partners including the active partner in the ratio of their capital investments.

Q6. Can partnership concept be extended to more than two partners?

Yes the same ratio and proportion rule for sharing profit and loss can be extended to three or more partners. For each partner calculate Capital multiplied by Time and then find the ratio of these values. Profit or loss is then shared in this ratio. If there is a loss the same method applies — just write loss in place of profit.

Q7. Which competitive exams ask partnership and share questions?

Partnership and share is asked in almost every competitive exam including CAT, SSC CGL, SSC CHSL, Bank PO, Bank Clerk, Railway RRB, CSAT and all state level competitive exams. It is closely related to Ratio and Proportion so mastering both topics together gives a significant advantage in exams.

Q8. Where can I practice partnership and share questions?

After understanding the concept you can practice on our Partnership and Share Exercise page which contains a large number of solved practice questions covering all types of partnership problems asked in competitive exams. You can also check our Profit Loss and Discount Concept page for related topics.