Partnership

🔹What is Partnership?

A partnership is a business arrangement in which two or more persons contribute money, labor, skill, or property to a business and share profits and losses according to an agreed-upon ratio.

🔹 Key Terms

Capital: The amount of money invested by each partner.
Profit or Loss: The net gain or deficit of the business.
Profit Sharing Ratio: The agreed ratio in which partners share profits or losses.
Time Period: The duration for which each partner's capital is invested (if unequal, the time must be taken into account).
Capital × Time: Used to calculate the effective investment of a partner if investments start or end at different times.

🔹Basic Formula for Profit Sharing

If partners invest capitals $C_1, C_2, \ldots, C_n$ for the same time period, their profit sharing ratio = ratio of capitals invested.

\text{Profit Ratio} = C_1 : C_2 : \ldots : C_n

If capitals are invested for different times $T_1, T_2, \ldots, T_n$ , profit sharing ratio =

C_1 \times T_1 : C_2 \times T_2 : \ldots : C_n \times T_n

🔹How to Calculate Individual Share of Profit?

\text{Individual's Share} = \frac{\text{Partner's Capital} \times \text{Time}}{\sum (\text{All partners' Capital} \times \text{Time})} \times \text{Total Profit}

🔹Important Cases and Examples

Case 1: Equal Time, Different Capitals

Example:
A and B invest ₹40,000 and ₹60,000 respectively for 1 year. Total profit is ₹20,000. Find A's share.

Solution:

\text{Profit ratio} = 40000 : 60000 = 2 : 3

Total parts = 2 + 3 = 5

A’s share = $\frac{2}{5} \times 20000 = ₹8000$

Case 2: Different Time Periods

Example:
A invests ₹50,000 for 6 months, B invests ₹40,000 for 1 year. Total profit is ₹18,000. Find B's share.

Solution:

Calculate capital × time (in months):

A: $50000 \times 6 = 300000$
B: $40000 \times 12 = 480000$

Profit ratio = 300000 : 480000 = 5 : 8

Total parts = 5 + 8 = 13

B's share = $\frac{8}{13} \times 18000 = ₹11076.92$

Case 3: One Partner Joins Late or Leaves Early

Calculate effective time for each partner’s capital, then calculate profit sharing as usual.

Case 4: Partner Withdraws Some Capital

Calculate the amount of capital and the time for which it was invested, then proceed.

🔹When a Partner Borrows Money from Another Partner

The borrowed amount is considered as a loan, and the lender gets interest on it.
The partner who borrows will not share profit on that amount.

🔹When Additional Capital is Introduced or Withdrawn

Calculate the profit-sharing ratio based on capital × time for each period separately.
Total profit is divided according to the combined ratio.

🔹Profit or Loss Sharing with Salaries and Interest on Capital

Sometimes partners receive salary or interest on capital.
Salary and interest are deducted from the total profit before sharing.
Remaining profit is shared according to profit ratio.

🔹 Important Formulas

Profit Share: $\frac{Capital \times Time}{Total Capital \times Time} \times Profit$
Time in months if given in years: multiply years by 12.
Adjust profit ratio accordingly if there are salaries or interest.

🔹 Practice Questions

A and B invest ₹30,000 and ₹20,000 respectively for 8 months and 6 months. Find the profit-sharing ratio.
A, B, and C invest ₹20,000, ₹30,000, and ₹50,000 respectively for 1, 2, and 3 years. Find the ratio of their profits.
A and B start a partnership with capitals ₹50,000 and ₹70,000. After 6 months, A withdraws ₹10,000. Total profit at the end of 1 year is ₹24,000. Find A’s and B’s shares.
A borrows ₹10,000 from B at 5% interest per annum. B invests ₹30,000 in business. The profit is ₹8,000. How much profit will B get if interest is paid first?

MakemyIQ