Introduction
Partnership Quiz 4 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
Rs.9750 are divided among K, L and M so that K may receive one half as much as L and M together receive and L receive one fifth of what K and M together receive. How much did M receive
- A. 4875
B. 2760
C. 3505
D. 3875
K = L + [latex]\frac {M}{2}[/latex]
L = K + [latex]\frac {M}{4}[/latex]
2 : 1 : 3 = [latex]\frac {9750 \times 3}{6} = 4875[/latex]
Q2
Sahir started a software business by investing Rs.30,000. After six months, Nikil Joined him with a capital of Rs.50,000. After 2 years, they earned a profit of Rs.22,500. What was Sahir’s share in the profit?
- A. Rs.10,800
B. Rs.9,700
C. Rs.11,500
D. Rs.10,000
[latex]30,000 \times 4 : 50000 \times 3 = 12 : 15 = 4 : 5 [/latex]
Sahir = [latex]\frac {22500 \times 4}{9} = 10000[/latex]
Q3
In a business Ishu invested 4 times that of Kathie and the period of investment of Ishu is 1/2 times that of Kathie. Then their profit ratio is:
- A. 1:2
B. 2:1
C. 3:1
D. 2:3
[latex]\frac {1}{2}[/latex] : 1 [latex]\Rightarrow[/latex] 1 : 2
Ratio of Profit = 4 : 2 = 2 : 1
Q4
A and B starts a business and invests 20000 & 30000 respectively. B is an active partner & he gets 25% of the profit separately. If their business yields them a total of 30000 as profit, what is the share of B at the end of a year?
- A. Rs 18,000
B. Rs 13,500
C. Rs 11,500
D. Rs 21,000
Ratio in which they get profits is 20,000 : 30,000 = 2 : 3
B gets 25% of 30,000 = 7,500
Profit left which is to be divided in ratio 2 : 3 = 30,000 - 7,500 = 22,500
Now N gets [latex]\frac {3}{(2 + 3)} \times 22,500 = 13,500[/latex]
So total share B = 7500 + 13500 = Rs 21,000
Q5
In a business A and C invested amounts in the ratio 3:2, whereas A and B invested amounts in the ratio 4:1. If the total profit at the end of a year is Rs 35,650, find the share of A.
- A. Rs 18,600
B. Rs 12,600
C. Rs 16,200
D. Rs 13,600
[latex]\frac {B}{A} = \frac {1}{4}, \frac {A}{C} = \frac {3}{2}[/latex]
So B : A : C = [latex]1 \times 3 : 4 \times 3 : 4 \times 2 = 3 : 12 : 8[/latex]
Share of A = [latex][\frac {12}{(3 + 12 + 8)}] \times 35,650[/latex] = Rs 18,600