Partnerships
Simple Partnership
Simple partnership - if money is invested for the same time period by various partners in a partnership .
In such a case, the gain or loss is distributed among the partners in the ratio of their investments.
If A and B invest Rs. x and Rs. y respectively for a given period, then at the end of that period:
(A’s share of profit) : (B’s share of profit) = x : y
Compound Partnership
Compound partnership - if the money is invested for different time periods by various partners in a partnership.
In such a case, the gain or loss is distributed among the partners in the ratio of product of their investments and time periods they invested their money for.
If A invests Rs. x for M years and B invests Rs. y for N years, then:
(A’s share of profit) : (B’s share of profit) = xM : yN
When investments are altered in the given period we need to take it into account while calculating profit-shares.
For example:
A and B invested Rs. 2000 and Rs. 3000 respectively for a year. If after four months A invested another Rs. 2000, then for the rest of the year A’s investment will be considered as Rs. 4000.
The ratio will come out to be:
A : B :: 40 : 36
Or A : B :: 10 : 9
Q. Aanya invested Rs. 50,000 in a business. After 9 months, Meenakshi joined her with a capital of Rs. 40,000. At the end of the year, what must have been the ratio in which the profit was divided between them?
(a) 2 : 5 (b) 5 : 1 (c) 2 : 3 (d) 3 : 4
Explanation:
Capital of Aanya worked for 12 months and Capital of Meenakshi worked for 3 months.
So, Effective investment of Aanya = Rs. 50,000 × 12
And Effective investment of Meenakshi = Rs. 40,000 × 3
We know that, Ratio of Profits = Ratio of Effective Investments
So, Ratio of Profits = (50,000 × 12)/(40,000 × 3) = 5/1
Therefore, the total profit must have been divided between them in the ratio of 5:1.
Answer: (b)
Have a look at the following peculiar example:
Incomes of Mr. A and Mr. B are in the ratio a : b, while their expenditure is in the ratio of x : y. Who saves more, if expenditure cannot exceed the income for either of them?
Let us consider some cases:
Case I:
Incomes of Mr. A and Mr. B are in the ratio 4 : 5, while their expenditure is in the ratio of 3 : 4.
If their incomes are 400 & 500 and expenditures are 30 & 40, then B saves more.
If their incomes are 400 & 500 and expenditures are 330 & 440, then A saves more.
Case II:
Incomes of Mr. A and Mr. B are in the ratio 4 : 5, while their expenditure is in the ratio of 5 : 6.
Here, B will always save more, in all circumstances.
Can we generalize this?