Ratio of Division of Gains:
1. 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) = \(x\) : \(y\)
Here investment of all partners are for same time, and the gain or loss is distributed among them in the ratios of their investments.
2. 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) = \(x\)p : \(x\)q
Here investments are for different time periods, equivalent capitals are calculated for a unit of time by taking,
(capital x number of units of time).
Profit or loss is divided in the ratio of these capitals.
Working partner: The partner one who works for the business is called a working partner.
Sleeping partner: The partner who simply invests the money for the business and doesn’t work is called a sleeping partner.
Here first person invested amount A for \(t_{1} \) period, second persons invested amount B for \(t_{2} \) period and so on.
Example 1:
A starts a business with Rs 2,000, B joins him after 3 months with Rs 4,000. C puts a sum of Rs 10, 000 in the business for 2 months only. At the end of the year the business gave a profit of Rs 5600. How should the profit be divided among them?
Solution:
Example 2:
A, B and C invested capital in the ratio 2 : 3 : 5, the timing of their investments being in the ratio 4 : 5 : 6. In what ratio would their profit be distributed?
Solution:
Example 3:
A, B and C invested capital in the ratio 5 : 6: 8. At the end of the business term, they received the profits in the ratio 5 : 3 : 12. Find the ratio of time for which they contributed their capital?
Solution:
2. Joseph, Johnson and Tom started a business each investing Rs. 20,000. After 5 months Joseph withdrew Rs.5000, Johnson withdrew Rs. 4000 and Tom invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the share of each.
Solution:
3. P, Q and R enter into partnership. P invests 2 times as much as Q invests and Q invests two- third of what R invests. At the end of the year, the profit earned is Rs. 7000. What is the share of Q?
Solution:
4. A, B, and C bought a plot for Rs. 2 lakh. A contributed Rs. 1,50,000 when they sold that from the profit, B got Rs. Rs. 5050 while C got Rs. 3000. What was the profit of A?
Solution:
5. P and Q started a business with capitals in the ratio of 5 : 8. After 2 months, Q took back his money. If they got profit in the ratio 3 : 6, for how many months P’s capital continued in the business?
Solution: