Introduction
Partnership Quiz 1 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
Three friends A, B, C invested in a business in the ratio of 4:5:6. After 6 months C withdraw half of his capital. If the sum invested by A is 36000, then the profit earned by C out of the total profit of 60000.
- A. 20000
B. 30000
C. 40000
D. 50000
sum invested by A = 4x = 36000.
X = 9000
Investment made by A, B , C – 36000, 45000, 54000
Ratio in which the profit will divide- [latex]36000 \times 12 : 45000 \times 2 : 54000 \times 6 + 27000 \times 6 [/latex]
i.e 4:5:9. So C share = [latex](\frac {9}{18}) \times 60000[/latex] = 30000
Q2
P, Q, R invested in the ratio of 6:5:7. After the end of business term they receive the profit in the ratio 3:1:5. Find the ratio of time in which they invested in the business.
- A. 34:14:50
B. 35:14:50
C. 35:50:14
D. 14:35:50
Take time as [latex]{t}_{1} {t}_{2}[/latex] and [latex]{t}_{3}[/latex]
[latex](\frac {6 \times {t}_{1}}{7 \times {t}_{1}}) = \frac {3}{1}[/latex], u will get [latex](\frac {{t}_{1}}{{t}_{2}}) = 5:2[/latex]
Similarly, [latex]( \frac {5 \times{t}_{2}}{7 \times {t}_{3}}) = \frac {1}{5}[/latex] u will get [latex]\frac {{t}^{2}}{{t}^{3}} = \frac {7}{25}[/latex]
Q3
3 persons enter into a partnership by investing in the ratio of 4:5:8. After 1 year A invest more 4300 and B withdraws 3200. Now, the ratio of investment changes to 5:4:7. Approximately how much A invested initially.
- A. 14555
B. 14655
C. 14755
D. 14855
After one year – 4x + 4300 : 5x - 3200 : 8x
So, to find X – [latex]\frac {(4x + 4300)}{(5x - 3200)} = \frac{5}{4}[/latex]
So investment made by A = [latex](\frac {33200}{9}) \times 4 = 14755.55 [/latex]
Q4
Three partners P, Q and R invest a total sum of 240000. At the end of the year A get 15000 rupee, B get 20000 and C get 25000 rupees as profit. How much amount is invested by A and C together.
- A. 10000
B. 13000
C. 16000
D. 18000
Ratio in which they get profit – 3:4:5
So total amount invested by A and C = [latex](\frac {8}{12}) \times 24000 = 16000[/latex]
Q5
Rahul got 5000 as his share out of the total profit of 9000. Ramesh had invested 3000 rupees for 6 months while rahul invested for the whole year. Find the amount invested by Rahul.
- A. 1875
B. 1975
C. 2125
D. 2275
Amount invested by rahul = P
[latex]12P : 3000 \times 6[/latex]
P : 1500
So Rahul share = [latex][\frac{p}{(1500 + p)}] \times 9000 = 5000[/latex]
[latex]P = 75 \times 25 = 1875[/latex]