When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership.
Ratio of Division of Gains :
(i) When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.
Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year: (A’s share of profit) : (B’s share of profit) = x : y.
(ii) When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital number of units of time). Now, gain or loss is divided in the ratio of these capitals.
Suppose A invests Rs. x for ‘p’ months and B invests Rs. y for ‘q’ months, then (A’s share of profit) : (B’s share of profit) = xp : yq.
(III) When investments are altered in the given period we need to take the changes into consideration while calculating their profits.
Suppose A and B started their business with Rs.5000 and Rs.10,000 respectively. If after three months A invested another Rs.5000 then we have to consider A's capital for the remaining period is Rs.10, 000
So A: B = (5000 X 3 + 10,000 X 9) : 10,000 X 12 = 1,05,000 : 1,20,000 = 7:8
3. Working and Sleeping Partners: A partner who manages the business is known as a working partner and the one who simply invests the money is a sleeping partner.
Ratio of Division of Gains :
(i) When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.
Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year: (A’s share of profit) : (B’s share of profit) = x : y.
(ii) When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital number of units of time). Now, gain or loss is divided in the ratio of these capitals.
Suppose A invests Rs. x for ‘p’ months and B invests Rs. y for ‘q’ months, then (A’s share of profit) : (B’s share of profit) = xp : yq.
(III) When investments are altered in the given period we need to take the changes into consideration while calculating their profits.
Suppose A and B started their business with Rs.5000 and Rs.10,000 respectively. If after three months A invested another Rs.5000 then we have to consider A's capital for the remaining period is Rs.10, 000
So A: B = (5000 X 3 + 10,000 X 9) : 10,000 X 12 = 1,05,000 : 1,20,000 = 7:8
3. Working and Sleeping Partners: A partner who manages the business is known as a working partner and the one who simply invests the money is a sleeping partner.
Questions and Solutions on above rules:
1. A, B, C enter into a partnership investing Rs. 35,000, Rs.45,000 and Rs.55,000 respectively. The respective shares of A, B, C in an annual profit of Rs.40,500 are
Solution : A : B : C = 35000 : 45000 : 55000 = 7 : 9 : 11.
A’s share = Rs (40500 x 7/27) = Rs. 10500
B’s share = Rs.(40500× 9/27) = Rs. 13500
C’s share = Rs.(40500×11/27)= Rs. 16500
2. In a business, Lucky invests Rs. 35,000 for 8 months and manju invests Rs 42,000 for 10 months. Out of a profit of Rs. 31,570. Manju’s share is :
Solution : ky: Manju = (35000 X 8) : (42,000 X 10) = 2:3
Manju’s share = Rs.3/5×31570 = Rs. 18,942
Manju’s share = Rs.3/5×31570 = Rs. 18,942
3. Amar started a business investing Rs. 70,000. Ramki joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?
Solution: Amar : Ramki : Sagar = (70000 X 36) : (105000 X 30) : (140000 X24) = 12 : 15 : 16.
Solution: Amar : Ramki : Sagar = (70000 X 36) : (105000 X 30) : (140000 X24) = 12 : 15 : 16.
4. A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdrawns Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?
Solution: A : B : C = (40,000 X 36) : (80,000 X 12 + 40,000 X 24) : (120,000 X 24 + 40,000 X 12) = 3: 4: 16
Solution: A : B : C = (40,000 X 36) : (80,000 X 12 + 40,000 X 24) : (120,000 X 24 + 40,000 X 12) = 3: 4: 16
5. Shekhar started a business investing Rs. 25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Shekhar invested another additional amount of Rs. 10,000 and Jatin joined them with an amount of Rs. 35,000. What will be Rajeev’s share in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 1999?.
Solution : Shekhar : Rajeev : Jatin = (25000 X 12 + 35000 X 12 + 45000 X 12) : (35000 X 24) : (35000 X 12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
Rajeev’s share = Rs.(150000×26) = Rs. 50000
Solution : Shekhar : Rajeev : Jatin = (25000 X 12 + 35000 X 12 + 45000 X 12) : (35000 X 24) : (35000 X 12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
Rajeev’s share = Rs.(150000×26) = Rs. 50000
6. A,B and C started a business with Rs.15000, Rs.25000 and Rs.35000 respectively. A was paid 10% of the total profit as a salary and the balance was divided in the ration of investment. If A’s share is Rs.4,200, then C’s share is:
Solution : A, B and C must divide their salaries in the ratio : 15,000 : 25,000: 35,000 = 3:5:7
Assume total Profit = 100X. then A share is 10% of 100X for managing business and 3/15 part of 90X for his investment (as the remaining profit is (100X - 10X = 90X)
So total A's share = 10X+315×90X=4,200
⇒X=150
Substituting X = 150 in 90X we get remaining profit for sharing. That is Rs.13,500
Now C's share = 715×13,500=Rs.6,300
Solution : A, B and C must divide their salaries in the ratio : 15,000 : 25,000: 35,000 = 3:5:7
Assume total Profit = 100X. then A share is 10% of 100X for managing business and 3/15 part of 90X for his investment (as the remaining profit is (100X - 10X = 90X)
So total A's share = 10X+315×90X=4,200
⇒X=150
Substituting X = 150 in 90X we get remaining profit for sharing. That is Rs.13,500
Now C's share = 715×13,500=Rs.6,300
