Partnership
When two or more persons invest some money for running a certain business together for a certain time and share the total profit at an agreed proportion.
Simple partnership
If all partners invest their money for the same time period.
Compound Partnership
If all partners invest their money for the different time period.
Sleeping Partner
A partner who only invests money and does not look after the business activities is called sleeping partner.
Active Partner
A partner who not only invests money but also takes part in the business activities is called an active partner.
Some Useful Shortcut Method
Rule- If two partners A and B invest ₹ IA and ₹ IB for the same period, then the ratio of their profit will be
| ⇒ | Profit of A | = | Investment of A |
| Profit of B | Investment of B |
| ⇒ | Profit of A : Profit of B = IA : IB |
Example- A and B start a business by investing ₹ 5000 and ₹ 8000 respectively. Find the ratio of their profit after 1 year.
Solution:- given, Investment of A = ₹
Investment of B = ₹ 8000
Profit will be distributed between A and B in the ratio of their investment.
| ⇒ | Profit of A | = | Investment of A |
| Profit of B | Investment of B |
| ∴ Ratio of their profit = | 5000 | = 5 : 8 |
| 8000 |
Example– A and B jointly start a business. The investment of A is equal to four times the investment of B. Find the share of A in the annual profit of ₹ 55000.
Solution:- Let the investment of B = ₹ x
Then, investment of B = ₹ 4x
| Profit of A | = | Investment of A | |
| Profit of B | Investment of B |
| = | 4x |
| x |
According to the question,
x + 4x = 55000
or, 5x = 55000
or, x = 55000/5
∴ x = 11000
∴ A’s share = 4x = 4 × 11000 = ₹ 44000
Rule- If two partners A and B invest ₹ IA and ₹ IB for the same period and earned total profit ₹ P, then
| A's share = |  |
 |
× p | |
| IA + IB |
| B's share = | |
|
× p | |
| IA + IB |
Example- A and B invested ₹16000 and ₹ 6000 for a period of 2 years. After 2 years, they earned ₹ 44000. What will be the share of A and B of this earning?
Solution:- given, Investment of A = ₹ 16000
Investment of B = ₹ 6000
Total Profit = ₹ 44000
| ∴ A's share = | |
|
× p | |
| IA + IB |
| = | |
|
× 44000 | |
| 1600 + 6000 |
| = | |
|
× 44000 | |
| 22000 |
= ₹ 32000
| ∴ B's share = | |
|
× p | |
| IA + IB |
| = | |
|
× 44000 | |
| 16000 + 6000 |
| = | |
|
× 44000 | |
| 22000 |
= ₹ 12000
Rule- If three partners A, B and C invest ₹ IA, ₹ IB, IC,…… for the same period, then the ratio of their profit will be
| Profit of A : Profit of B : Profit of C : …… = IA : IB : IC : .......... |
Example- A, B and C start a business by investing ₹ 5000, ₹ 8000 and ₹ 10000 respectively. Find the ratio of their profit after 2 years.
Solution:- given, IA = ₹ 5000
IB = ₹ 8000
IC = ₹ = ₹ 10000
| Ratio of Profit = IA : IB : IC |
= 5000 : 8000 : 10000
= 5 : 8 : 10
Rule- If three partners A, B and C invest ₹ IA, ₹ IA and ₹ IC for the same period and earned total profit ₹ P, then
| A's share = | |
|
× p | |
| IA + IB + IC |
| B's share = | |
|
× p | |
| IA + IB + IC |
| C's share = | |
|
× p | |
| IA + IB + IC |
Example- A, B and C invested ₹5000 and ₹ 7000 and ₹ 8000 for a period of 2 years. After 2 years, they earned ₹ 60000. What will be the share of A, B and C of this earning?
Solution:-
given, Investment of A = ₹ 5000
Investment of B = ₹ 7000
Investment of C = ₹ 8000
Total Profit = ₹ 60000
| A's share = | |
|
× p | |
| IA + IB + IC |
| = | |
|
× 60000 | |
| 5000 + 7000 + 8000 |
| = | |
|
× 60000 | |
| 20000 |
= 5000 × 3
= ₹ 15000
| B's share = | |
|
× p | |
| IA + IB + IC |
| = | |
|
× 60000 | |
| 5000 + 7000 + 8000 |
| = | |
|
× 60000 | |
| 20000 |
= 7000 × 3
= ₹ 21000
| C's share = | |
|
× p | |
| IA + IB + IC |
| = | |
|
× 60000 | |
| 5000 + 7000 + 8000 |
| = | |
|
× 60000 | |
| 20000 |
= 8000 × 3
= ₹24000
Rule- If two partners A and B invest ₹ IA and ₹ IB for the different time period t1 and t2, then the ratio of their profit will be
| Profit of A : Profit of B = IA × t1 : IB× t1 |
Example- A starts a business with ₹ 4000 and B joins him after 4 months with ₹ 7000. Find the ratio of their profits at the end of the year.
Solution:- Here, A invest for 1 year = 12 months
B invest after 3 months = ( 12 - 4 ) = 8 months
| Ratio of profit A and B = IA × t1 : IB × t2 |
= 4000 × 12 : 7000 × 8
= 6 : 7
Example-A Starts a business with ₹ 3000 and B joins the business 4 months later with an investment of ₹ 8000. After 1 year, they earn a profit of ₹ 14000. Find the share of A and B.
Solution:- A invest for 1 year = 12 months
B invest after 6 months = ( 12 - 6 ) = 6 months
| Ratio of Profit A : Profit B = IA × t1 : IB × t2 |
= 3000 × 12 : 8000 × 6
= 3 : 4
Let the share of A = 3x and share of B = 4x
According to the question,
3x + 4x = 14000
or, 7x = 14000
or, x = 14000/7 = 2000
∴ A's share = 3x = 3 × 2000 = ₹ 6000
∴ B's share = 4x = 4 × 2000 = ₹ 8000