Partnership :
Partnership is an association of two or more parties, they put money for business.
Division of Profit and Loss:
Rule : When investment of all partners are for the same time, the loss or profit is distributed among partners in the ratio of investment.
Ex. Let P and Q invested Rs. a and b for one year in a business then share of profit and loss be ,
P's share of profit : Q's share profit = a : b
Rule : When investments are for different time period, then profit ratio is calculated as capital multiplied by length of investment
Ex. P's share of profit : Q's share profit = a* t1 : b* t2
Ex. Three partners A, B and C invested Rs. 1000, Rs. 1200 and Rs. 1500 respectively in business for one year. How should they divide a profit of Rs. 1295 ?
Solution : As investment period is same so, profit should be divided in ratio of capitals as, 10 : 12 : 15, also 10 + 12 + 15 = 37
Ex. A, B and C enter into a business. A put Rs. 1000 for 6 months, B puts Rs. 1200 for 8 months and C puts Rs. 1400 for 10 months. Their gain was Rs. 666 . Find out the share of each partners.
Solution : Ratio of profits will be 10*6 : 12*8 : 14*10 = 60 : 96 : 140 = 15 : 24 : 35
Ex. Three friends Ram, shyam and mohan enter into partnership. Ram put one forth of capital for one fourth of the time. Shyam puts one third of capital for one half of time. Shyam puts remaining capital for full period of time. Find the division of profit Rs. 806 among three friends.
Solution : Ram's share : Shyam's share : Mohan's share =
Now LCM of 16, 6, 12 is 48, so multiplying the equation by 48 we get ratio as 3 : 8 : 20 , also 3 + 8 + 20 = 31
Ex. A, B and C enter into a partnership and their shares are in ratio 1/2 : 1/3 : 1/4, after 2 months, A withdraws half of his capital and after 10 months, a profit of Rs 378 is divided among them. What is B's share ?
Solution : Ratio of investments =1/2 : 1/3 : 1/4 , now LCM of 2, 3, 4 is 12 on multiplying the ratio with 12 we get 6 : 4 : 3 , also we assume their initial investment be 6x, 2x and 3x so, we can write: A : B :C
Ex. A and B are partners in a business. A contributes 1 / 4 of the capital for 15 months and B received 2 / 3 of the profit, for how long B's money was used ?
Solution : Let total profit is x
Let total capital invested be Rs P and A's money was used for 15 months while B's money was used for b months then we can write the equation as-
So, B's money was used for 10 months
Ex. A began a business with Rs. 21, 000 and is joined afterwards by B with Rs. 42,500. For how much period does B join, If the profits at the end of the year are divided in the ratio 3 : 1 ?
Solution : Let B joined for P months
then we can write equation as - ( 85,000 * 12 ) : ( 42,500 * P ) = 3 : 1
Ex. In a business A and C invested amounts in the ratio 2 : 1, whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs. 56,914 was their profit, how much amount did B receive ?
Solution : A : B = 3 : 2 , A : C = 2 : 1
B : A = 2 : 3 , B : A = 4 : 6
Now, A : C = 2 : 1, A : C = 6 : 3 , So B : A : C = 4 : 6 : 3
We can write as A : B : C = 6 : 4 : 3
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