Introduction
Partnership Quiz 7 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
A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is:
- A. 500
B. 1000
C. 1500
D. 2000
Let the total profit be Rs. 100.
After paying to charity, A's share = [latex] (\frac {95 \times 3}{5}) = Rs. 57[/latex]
If A's share is Rs. 57, total profit = Rs. 100.
If A's share is Rs. 855, total profit = [latex](\frac {100}{57 \times 855}) [/latex] = 1500.
Q2
A, B, C started a business with their investments in the ratio 1:3 :5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investments. The ratio of their profits at the end of the year is
- A. 1 : 2 : 3
B. 3 : 4 : 15
C. 3 : 5 : 10
D. 5 : 6 : 10
Let their initial investments be x, 3x and 5x respectively. Then,
A : B : C = [latex] (x \times 4 + 2x \times 8) : (3x \times 4 + (\frac {3x}{2}) \times 8) : (5x \times 4 + (\frac {5x}{2}) \times 8)[/latex]
20x : 24x : 40x = 5 : 6 : 10
Q3
A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
- A. 45
B. 50
C. 55
D. 60
A : B : C = (10 × 7) : (12 × 5) : (15 × 3)
= 70 : 60 : 45
= 14 : 12 : 9
C's rent = Rs.[latex] (\frac {175 \times 9}{35})[/latex]
= Rs. 45
Q4
A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?
- A. 4 months
B. 5 months
C. 6 months
D. 8 months
Suppose B joined for x months.
Then, [latex] \frac {(85000 \times 12)} {(42500 \times x)} = 3. [/latex]
Or x = [latex]\frac{(85000 \times 12)}{(42500 \times 3)} = 8[/latex]
So, B joined for 8 months.
Q5
If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 4650, C will receive ____
- A. Rs. 700
B. Rs. 800
C. Rs. 900
D. Rs. 1000
Let 4A = 6B = 1OC = k. Then, [latex] A = \frac {k}{4}, B = \frac {k}{6}, and C = \frac {k}{10}[/latex]
A : B :C = [latex]\frac {k}{4} : \frac {k}{6} : \frac {k}{10}[/latex] = 15 : 10 : 6.
Hence, C's share [latex](\frac {4650 \times 6}{31})[/latex] = Rs, 900.