Partnership Quiz 9 | Quantitative Aptitude

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Partnership Quiz 9 | Quantitative Aptitude

Introduction

Partnership Quiz 9 | Quantitative Aptitude 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

X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?

Q1 - Answer

Explanation - 1

Ratio of the investment
= 21000:17500 = 210:175 = 42:35 = 6:5
Share of X in the profit
= [latex] 26400 \times \frac {6}{11} = 2400 \times 6 = 14400[/latex]

Q2

X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?

Q2 - Answer

Explanation - 2

Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
= [latex] 45000 \times 12:30000 \times 9[/latex]
= [latex] 45 \times 12:30 \times 9[/latex]
= [latex] 3 \times 12:2 \times 9[/latex]
= 2:1

Q3

A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?

Q3 - Answer

Explanation - 3

Total amount invested = 50000
Assume that investment of C = x
Then investment of B = 5000 + x
Investment of A = 4000 + 5000 + x = 9000 + x
x + 5000 + x + 9000 + x = 50000
⇒ 3x + 14000 = 50000
⇒3x = 50000 – 14000 = 36000
⇒ x = [latex]\frac {36000}{3} = 12000[/latex]
Investment of C = x = 12000
Investment of B =5000 + x = 17000
Investment of A = 9000 + x = 21000
Ratio of the investment of A, B and C
= 21000:17000:12000
= 21:17:12
Share of A = Total profit [latex]\times \frac { 21}{50}[/latex]
= [latex] 35000 \times \frac { 21}{50}= 700 \times 21=14700[/latex]