Introduction
Partnership Quiz 5 chapter deals with profit and loss related problems. Profit and/or loss is shared among the partners based on the sum of money invested by individual partners and the time period of the investment.
For example: A partner who has invested the highest amount of money/resources will receive the highest share of the profit at the end of the year provided all the partners have invested for the same time period.
Ratio of Division of Gains:
1. Suppose A and B invest Rs. [latex]x[/latex] and Rs. [latex]y[/latex] respectively for a year in a business, then at the end of the year:
(A's share of profit) : (B's share of profit) = [latex]x[/latex] : [latex]y[/latex]
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. [latex]x[/latex] for 'p' months and B invests Rs. [latex]y[/latex] for 'q' months, then
(A's share of profit) : (B's share of profit) = [latex]x[/latex]p : [latex]x[/latex]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.
Concept 1: If a group of n persons invested different amount for different period then their profit is the ratio is [latex]At_{1}[/latex] : [latex]Bt_{2} [/latex] : [latex]Ct_{3} [/latex] : [latex]Ct_{3} [/latex] : [latex]Dt_{4} [/latex] : …… : [latex]Xt_{n} [/latex]
Here first person invested amount A for [latex]t_{1} [/latex] period, second persons invested amount B for [latex]t_{2} [/latex] period and so on. Q1
Smith and Kate started a business investing Rs. 84,000 and Rs. 28,000 respectively. In what ratio the profit earned after 2 years be divided between Smith and Kate respectively?
- A. 2 : 3
B. 3 : 1
C. 13 : 3
D. None of these
[latex]\frac {P’s share of profit}{Q’s share of profit} = \frac {x}{y}[/latex].......(x and y are investments)
x : y = P’s share of profit : Q’s share of profit
Therefore,
[latex]\frac {Smith’s share of profit }{Kate share of profit} = \frac {84000}{28000} = \frac {3}{1}[/latex]
The profit earned after 2 years will be divided between Smith and Kate in the ratio of 3 : 1.
Q2
Sham and Ram invested in a business and gained a profit which was divided in the ratio of 2 : 3. If Sham invested Rs. 40,000, then what was the amount invested by Ram?
- A. Rs. 30,000
B. Rs. 45,000
C. Rs. 60,000
D. Rs. 75,000
[latex]\frac {P’s share of profit}{Q’s share of profit} = \frac {x}{y}[/latex].......(x and y are investments)
x : y = P’s share of profit : Q’s share of profit
Therefore,
[latex]\frac {Sham’s share of profit}{Ram’s share of profit} = \frac {84000}{28000} = \frac {Sham’s investment}{Ram’s investment}[/latex]
[latex]\frac {2}{3} = \frac {4000}{X}[/latex]
X = Rs. 60,000
Amount invested by Ram = Rs. 60,000
Q3
John, Tyson and Mike started a business by investing Rs.1,00,000, Rs. 1,50,000 and Rs. 1,75,000 respectively. Find the share of Mike, out of an annual profit of Rs. 46,000.
- A. Rs. 15941. 93
B. Rs. 16943. 59
C. Rs. 18941. 17
D. Rs. 19971. 03
Here, three partners invest together and earn a profit of Rs. 46,000 at the end.
Hint: Ratio of shares of John, Tyson and Mike = Ratio of their investments
Therefore,
100000 : 150000 : 175000 = 4 : 6 : 7
Now, we have to calculate share belonging to each person from all the shares considering the annual profit.
Total shares = 4 + 6 + 7 = 17 shares
John’s Share = [latex]\frac {4}{17} × 46000 = Rs. 10823.53[/latex]
Tyson’s Share = [latex]\frac {6}{17} × 46000 = Rs. 16235.294[/latex]
Mike’s Share = [latex]\frac {7}{17} × 46000 = Rs. 18941.176[/latex]
Q4
Harry, John and Smith start a shop by investing Rs. 27,000. Rs. 72,000 and Rs. 81,000 respectively. At the end of the year, the profit was distributed among them and Smith earns the share of Rs. 36,000. Find the total profit.
- A. Rs. 1,10,000
B. Rs. 1,2,5000
C. Rs. 98,000
D. Rs. 80,000
Hint: Ratio of shares of Harry, John and Smith = Ratio of their investments
Harry : John : Smith = 27000 : 72000 : 81000 = 3 : 8 : 9
Given: Share of profit earned by Smith = Rs. 36,000
Total no. of shares = 3 + 8 + 9 = 20 shares
Smith’s share = [latex]\frac {9}{20}[/latex]
Let total profit = Rs. X
[latex]\frac {36000}{x} = \frac {9}{20}[/latex]
[latex]\frac {36000 \times 20}{9} = 80000[/latex]
Total profit = Rs. 80,000
Q5
George started a hardware business by investing Rs. 50,000. After six months, Kate joined him with a capital of Rs. 70,000. After 3 years, they earned a profit of Rs. 25,000. Find George’s share in profit.
- A. Rs. 13000.00
B. Rs. 13224.65
C. Rs. 12500.50
D. Rs. 11538.46
This type of partnership is called as compound partnership. George invested for 3 years (36 months) and Kate for 2 years 6 months (30 months). After George’s investment for 36 months and Kate’s investment for 30 months, both get a profit of Rs. 25,000.
Hint:
[latex]\frac {George’s share of profit}{Kate’s share of profit} = \frac {Initial investment of George × Time}{Initial investment of Kate × Time}[/latex]
Always try to simplify this type of numerical by arranging them in table format as shown below:
Actual investment ratio of George and Kate = [latex]\frac {Actual investment of George}{Actual investment of Kate} = \frac {1800000}{2100000} =\frac {6}{7} [/latex]
George’s share of profit = [latex]\frac {6}{13} \times 25000= Rs. 11538.46[/latex]
| George | Rs. 50.000 for 3 years | Actual investment = initial investment × months = 50000 × 36 = Rs. 1800000 |
| Kate | Rs. 70.000 for 2 years 6 months | Actual investment = initial investment × months = 70000 × 30 = Rs. 2100000 |