Introduction
Partnership Quiz 8 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
Raju & Ashok are partners in a business. Raju contributes 2/5 of the capital for 5 months and Ashok received ¾ of the profit. For how long Ashok’s money was used?
- A. 10 months
B. 6 months
C. 7 months
D. 8 months
Let the total profit be Rs.z
Then Ashok’s share = Rs. [latex]\frac {3z}{4}[/latex]
Raju’s share =[latex] z – \frac {3z}{4}[/latex]
=[latex]\frac {z}{4}[/latex]
Therefore Raju : Ashok = [latex]\frac {z}{4} : \frac {3z}{4}[/latex]
=z:3z
=1:3
Let the total capital be rs.x and
Suppose Ashok’s money was used for x months
Then, [latex]\frac {(\frac {2x}{5}) \times 5 }{ (\frac {3x}{5}) \times y} = \frac {1}{3}[/latex]
[latex]\frac {10x}{3xy} = \frac {1}{3}[/latex]
10 = y
Thus Ashok’s money was used for 10 months.
Q2
Anu & Aarthi started a business with initial investments in the ratio of 15:8 and their annual profits were in the ratio 45 : 16. If anu invested the money for 6 months for how many months did Aarthi invest her money?
- A. 3 months
B. 4 months
C. 5 months
D. 6 months
Suppose Anu invested Rs.15x for 6 months &
Aarthi invested Rs.8x for y months
Then, [latex]\frac {15x \times 6 }{8x \times y} = \frac {45}{16}[/latex]
Y = 4 months
Hence Aarthi invested the money for 4 months.
Q3
Keerthi and her friend kavi invested in the ratio 7:5 in a business. If 16% of the profit is given to charity and Keerthi’s share is Rs.2352 then what will be the total profit ?
- A. Rs.1600
B. Rs.2400
C. Rs.3600
D. Rs.4800
Keerthi and her friend kavi invested in the ratio 7:5
7’s = 2352
1’s = 336
12’s = 4032
84 % of profit = 4032
[latex](\frac {84}{100}) \times [/latex] Total profit = 4032
Total profit = [latex]4032 \times (\frac {100}{84})[/latex] = 4800
Q4
Aakash, Murali and sakthi started a business by investing Rs. 153000 Rs. 126000 and Rs.174000 respectively. Find the share of each persons, out of an annual profit of Rs. 75500
- A. Rs 25500, 21000, 29000
B. Rs 23000, 19000, 27000
C. Rs 27500, 23000, 31000
D. Rs 20000, 16000, 25000
Ratio of share Aakash, Murali and sakthi = Ratio of their investment
Aakash: Murali : sakthi = 153000:126000:174000
=153:126:174
=51:42:58
Aakash share = Rs [latex](\frac {75500 \times 51}{151})[/latex]
= Rs [latex](500 \times 51)[/latex]
= RS 25500
Murali share = Rs [latex](\frac {75500 \times 42}{151})[/latex]
= Rs [latex](500 \times 42)[/latex]
= Rs 21,000
Sakthi share = Rs [latex](\frac {75500 \times 58}{151})[/latex]
= Rs [latex](500 \times 58)[/latex]
= Rs 29,000
Q5
P, Q and R started a hotel business in which P invested Rs.7500 for 2year, Q invested Rs.15000 for 3 years, R invested Rs.22500 for 4 years. At the end of 4 years, the profit received by them is Rs.4200. What is R’s share?
- A. Rs 1260
B. Rs 2840
C. Rs 2520
D. Rs 2400
P = Rs.7500/- per 2 years
Q = Rs.15000/- per 3 years
R= Rs.22500/- per 4years
P:Q:R = (7500 [latex]\times[/latex] 2): (15000 [latex]\times[/latex] 3):(22500 [latex]\times[/latex] 4)
P:Q:R = 15000:45000:90000
P:Q:R =15:45:90
P:Q:R =1:3:6
Then, R’s share is,
=Rs [latex](\frac {6}{10 \times 4200})[/latex]
=Rs 2520
Hence the required answer is Rs 2520