IMPORTANT FACTS AND FORMULAE
1. Partnership :: When two or more than two persons start or run a business jointly, at that time they are called partners and the deal between/among them is known as partnership.
2. Ratio of Division of Gains:
(i) When the investments of all the partners are for the same time, the loss or gain is distributed a among the partners in the ratio of their investments.
Let A and B invest Rs. x and Rs. y respectively for a year in a particular business, then at the end of the year ::
(A’s share of profit) : (B's share of profit) = x : y.
(ii) When the investments are for different time periods, then the equivalent capitals are calculated for a unit of time by taking (capital x number of units of time).
Now, gain or loss is divided into the ratio of these capitals.
Let A invests Rs. x for m months and B invests Rs. y for n months, then
(A’s share of profit) : (B's share of profit) = xm : yn.
3. Working and Sleeping Partners :: A partner who mainly manages all the business is known as a working partner and on the other hand the one who simply invests the money is known as sleeping partner.
SOLVED EXAMPLES
Ex. 1. Shubham, Himanshu and Arpit started a business by investing Rs. 1,20,000, Rs. 1,35,000 and ,Rs.1,50,000 respectively. Find out the share of each, out of an annual profit of Rs.56,700.
Sol. Ratio of shares of A, Band C = Ratio of their investments
= 120000 : 135000 : 150000 = 8 : 9 : 10.
Shubham’s share = Rs. (56700 x (8/27))= Rs. 16800.
Himanshu's share = Rs. ( 56700 x (9/27)) = Rs. 18900.
Arpit's share = Rs. ( 56700 x (10/27))=Rs. 21000.
Ex. 2. Shubham, Himanshu and Arpit start a business each investing Rs. 20,000. After 5 months Shubham withdrew Rs.6000 Himanshu withdrew Rs. 4000 and Arpit invests Rs. 6000 more. At the end of year, a total profit of Rs. 69,900 was recorded. Find the share of each.
Sol. Ratio of the capitals of Shubham, Himanshu and Arpit
= 20000 x 5 + 15000 x 7 : 20000 x 5 + 16000 x 7 : 20000 x 5 + 26000 x 7
= 205000:212000 : 282000 = 205 : 212 : 282.
Shubham’s share = Rs. 69900 x (205/699) = Rs. 20500 I
Himanshu's share = Rs. 69900 x (212/699) = Rs. 21200;
Arpit's share = Rs. 69900 x (282/699) = Rs. 28200.
Ex. 3. Shubham, Himanshu and Arpit enter into partnership. Shubham invests 3 times as much as Himanshu and Himanshu invests two-third of what Arpit invests. At the end of the year, the profit of Rs. 6600 was recorded. What is the share of B ?
Sol. Let Arpit's capital = Rs. x. Then, Himanshu's capital = Rs. (2/3)x
Shubham’s capital = Rs. (3 x (2/3).x) = Rs. 2x.
Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.
Hence, Himanshu's share = Rs. ( 6600 x (2/11))= Rs. 1200.
Written
In Aptitude, Concepts, Partnership
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