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Partnership is an association of two or more persons who put their money together to carry on some business.
If capitals of partners are invested for the same period, the partnership is called simple. If the period of investment is the same for each partner, then profit or loss in divided in the ratio of their investments.
a) If A and B are partners in a business then
investment of A / Investment of B = Profit of A / Profit of B
= Loss of A / Loss of B
b) If A, B and C are three partners then
Profit of A : Profit of B : Profit of C
Or loss of A : Loss of B ; Loss of C is equal to
Investment of A : Investment of B : Investment of C
If the capitals of partners are for different periods, partnership is called compound.
If period of investment is different, then profit or loss is divided in the ratio of the product of capital and the period for which invested.
For example (a): If A and B are partners in business then
Capital x period for A / Capital x period for B
= profit of A / Profit of B
= Loss of A / Loss of B
b) If A, B and C are partners then
capital x period for A : Capital x period for B
: capital x period for C
= Profit of A : Profit of B : Profit of C
= Loss of A : Loss of B : Loss of C
It is the product of the capital invested and the period for which it is invested
A working partner is the one who manages the business.
Is the one who provides capital but does not attend to the business
(i) If investments are in the ratio a : b : c and timings of their investment are in the ratio x : y : z then profit or loss is divided in the ratio ax : by : cz
ii) If investments are in the ratio a : b : c and profits are in the ratio p : q : r then ratio of times is p/a : q / b : r / c
iii) If the ratio of periods of investment are t1 : t2 : t3 and their profits are in the ratio a : b : c, then their capitals will be in the ratio a/t1 : b/t2 : c/t3
Ram, Mohan and Santosh together started a business in partnership.
The ratio of their capital is 3 : 4 : 7. If profit after one year is Rs. 21000, what will be Ram’s share in the profit.
Sol: sum of proportions= 3 + 4 + 7 = 14
So Ram’s Share = 3/14 x 21000 = Rs. 4500
A and B start a business by investing Rs. 4000 and Rs. 12000 respectively. Find the ratio of their profit after one year.
Sol: The profit will be divided in the ratio of the capital
So ratio is 4000 : 12000 or 1 : 3
A and B invested Rs. 24000 and Rs. 8000 for a period of 2 years and saved Rs. 48000. What will be their share respectively.
Sol: Profit will be divided in the ratio of their capital i.e. 24000 : 8000 or 3 : 1
A will get ¾ x 48000 = 36000
B will get ¼ x 48000 = 12000
A and B started a business and A invested 3 times the amount as compared to B. Find their share in the annual profit of Rs. 52000.
Sol: Profit will be divided in the ratio of their investment i.e.
3 : 1
So A’s share is ¾ x 52000 = Rs. 39000
B’s share is ¼ x 52000 = Rs. 13000
A started a business and invested Rs. 2000. After 3 months B joined him and invested Rs. 8000. Find the ratio of their profit at the end of the year.
Sol: A’s share : B’s share
= 2000 x 12 : 8000 x 9
= 24000 : 72000
= 1 : 3
A started a business with Rs. 5000 and B jointed after 4 months with Rs. 4000. After a year they earn a profit of Rs. 23000.
Find the share of A and B respectively.
Solution: A invested Rs. 5000 for 12 months = 5000 x 12
B invested Rs. 4000 for 8 months = Rs. 4000 x 8
Ratio of profit 60000 : 32000 i.e. 15 : 8
A’s share in Rs. 23000 = 15/23 x 23000 = Rs. 15000
B’s share in Rs. 23000 = 8 /23 x 23000 = Rs. 8000
A started business with Rs. 2000. After 3 months B joins with Rs. 4000. C invested a sum of Rs. 10000 for 2 months only. How will they divide profit of Rs. 8000 after one year.
Sol: A invested Rs. 2000 for 12 months = 2000 x 12 = 24000
B invested Rs. 4000 for 9 months = 4000 x 9 = 36000
C invested Rs. 10000 for 2 months = 10000 x 2 = 20000
Share will be divided in the ratio
24000 : 36000 : 20000
6 : 9 : 5
A’s share in profit of Rs. 8000 = 6/20 x 8000 = Rs. 2400
B’s share in profit of Rs. 8000 = 9 / 20 x 8000 = Rs. 3600
C’s share in profit of Rs. 8000 = 5/20 x 8000 = Rs. 2000
A, B, C invested capital in the ratio 2 : 3 : 5. At the end they received profit in the ratio of 5 : 3 : 12. Find the ratio of the time for which they invested their capital.
Sol: Ratio in profit = 5 : 3 : 12
Ratio in investment = 2 : 3 : 5
Ratio in times will be 5/2 : 3/3 : 12/5
Or 5/2 : 1 : 12 / 5
Multiply by 10
25 : 10 : 24
A, B, C invested money for time periods in the ratio of 5 : 6 : 8 and earned profit in the ratio of 5 : 3 : 12. Find the ratio of investment of A, B and C
Sol: Ratio of profit 5 : 3 : 12
Ratio of time periods 5 : 6 : 8
So ratio of investments 5/5 : 3/6 : 12/8
Or 1 : ½ : 3/2 or 2 : 1 : 3