Chapter 3 Partnership Business Solved Example Problems
What is a simple partnership business?
Simple partnership business
If two or more than two persons investing their own capitals start a business together, then this type of business is called partnership business. The amount of money invested in the business by each of the partners are called their own capital of the individual partners.
There are two types of partnership business—
- Simple Partnership Business; And
- Compound Partnership Business.
WBBSE Solutions for Class 10 Maths
1. Simple Partnership Business
If in a partnership business, the capital of each partner is invested for the same period of time, then the profit or loss is distributed according to their invested capital. This type of business is called the simple partnership business.
2. Compound Partnership Business
If in a partnership business, the capitals of different partners are invested for different periods of time, then the profit and loss is distributed amongst the partners according to the capitals invested by each of them, considering the period of time for which their capitals were invested.
In this case, the proportion of the profit or less of the partners will be the product of their capitals by their respective period of times. This type of business is called compound partnership business.
Partnership Business Is Based Upon The Following Principles
- Capital The total amount of capital is either collected equally from the partners or at a definite proportion decided unanimously on the before.
- Profit Or Loss Distribution
(a) May be distributed equally;
(b) May be distributed according to their corresponding proportion of capitals, or
(c) May be distributed according to any other contact taken unanimously earlier. If their is no mention of any definite type of contact taken by the partners, then it will be let that the profit or loss will be distributed according to the proportion of capitals invested by the partners in the business. - Yearly Or Half-Yearly Allowance If to manage the business each or anyone of the partners give their efforts to the business, then an yearly or half-yearly allowance is paid to the partner concern as per contract taken by the partners unenimously. After paying this allowance, the rest of the profit is distributed among the partners.
Chapter 3 Partnership Business Solved Example Problems Ex. 1. Very Short-Answer Type Questions
Multiple Choice Questions (MCQ)
“WBBSE Class 10 Partnership Business solved examples”
Question 1. Sumita, Shreya and Smita started a business by investing total ₹ 6000. After a year Sumita, Shreya and Smita get profit share of ₹ 50, ₹ 100 and ₹ 150 respectively. Smita invested in this business.
(a) 1000
(b) 2000
(c) 3000
(d) 4000.
Solution
Given
Sumita, Shreya and Smita started a business by investing total ₹ 6000. After a year Sumita, Shreya and Smita get profit share of ₹ 50, ₹ 100 and ₹ 150 respectively.
Sumita’s profit Shreya’s profit Smita’s profit
= 50: 100: 150
= 1: 2: 3
Hence, Smita’s investment = ₹ \(\left(6000 \times \frac{3}{1+2+3}\right)\)
= ₹ \(6000 \times \frac{3}{6}=₹ 3000 .\)
(c) is correct.
Smita invested in this business is 3000
Question 2. Amal and Bimal started a business. Amal invested some money for 6 months. If they make a profit of share of 46, the capital of Bimal in the business is
(a) 1500
(b) 3000
(c) 4500
(d) 6000.
Solution:
Given
Amal and Bimal started a business. Amal invested some money for 6 months. If they make a profit of share of 46,
Total profit ₹69
Profit of Bimal is ₹ 46
∴ Profit of Amal = ₹(69 – 46) = ₹ 23
∴ Profit of Amal : Profit of Bimal = 23 : 46 = 1 : 2
∴ Capital of Amal : Capital of Bimal = 1 : 2
∴ Capital of Amal with respect of 1 month = ₹ 500 x 9 = ₹4500
∴ Capital of Bimal with respect of 1 month = ₹ \(4500 \times \frac{3}{1} \times \frac{2}{1+2}=₹ 9000\)
Since Bimal invested his capital for 6 months,
∴ Capital of Bimal = ₹(9000 ÷ 6) = ₹1500.
(a) is correct.
The capital of Bimal in the business is 1500.
“Partnership problems with solutions for Class 10 Maths”
Question 3. In a business capital of A is double the capital of B and capital of B is 4 times the capital of C. Then the ratio of their profit is—
(a) 148
(b) 248
(c) 8 24
(d) 84 1.
Solution
Given
In a business capital of A is double the capital of B and capital of B is 4 times the capital of C.
Let the capital of C be x.
∴ The capital of B is ₹ 4x and the capital of A is ₹ 8x.
The ratio of capital of A, B, C = 8x: 4x : x
= 8: 4: 1
Hence, the ratio of profit is 8 : 4: 1.
Question 4. In a partnership business, Amal invested capital double the capital of Palash. The ratio of the period of investment is 1/2 1/3 Then the ratio of their profit is—
(a) 13
(b) 31
(c) 61
(d) 2 3.
(d) is correct.
Solution
Given
In a partnership business, Amal invested capital double the capital of Palash. The ratio of the period of investment is 1/2 1/3
(Amal’s investment period) (Palash’s investment period)=1/2 :1/3= 3:2
Let Amal invested for 3x months and Palash, invested for 2x months.
Also, let capital of Palash is y
Capital of Amal is ₹ 2y
∴ Amal’s profit Bimal’s profit = 3x × 2y 2x × y = 6xy : 2xy
= 3:1
∴ (b) is correct.
The ratio of their profit is 3:1
Question 5. The total capital in a business is 50000. If A 5000 more than C, then the profit becomes
(a) 8400
(b) 4900
(c) 13600
(d) 14700.
Solution
Given
The total capital in a business is 50000. If A 5000 more than C
Let capital of C be x.
∴ Capital of B is (x + 5000) and capital of A is (x + 9000)
∴ x + x + 5000 + x + 9000 = 50000
⇒ 3x+14000 = 50000
⇒ 3x= 36000 ⇒ x = 36000 /3 = 12000
The capitals of A, B and C are (12000 + 9000) = 21000, (12000 + 5000) = 17000 and 12000 respectively.
Ratio of the capitals of A, B and C In 35000, the profit of
= 21000: 17000: 12000
= 21:17 : 12
A = 35000 × (21 /(21+17+12))
= 35000 X ( 21/50)
=14700.
(d) is correct.
The profit becomes 14700.
Chapter 3 Partnership Business Solved Example Problems Ex. 2. Short Answer Type Questions
“Chapter 3 Partnership Business exercises WBBSE”
Question 1. The total profit is ₹1500 in a partnership business of Rajib and Rahul. If the capital of Rajib is 6000 and profit is ₹900. Calculate the capital of Rahul.
Solution
Given :
The total profit is ₹1500 in a partnership business of Rajib and Rahul. If the capital of Rajib is 6000 and profit is ₹900.
Total profit = ₹ 1500
Rajib’s profit = ₹ 900
∴ Rahul’s profit = ₹ (1500 – 900) = ₹ 600
∴ If the profit be ₹ 900, then capital = ₹ 6000
∴ If the profit be 1, then capital =₹ (6000/900)
∴ If the profit be 600, then capital = ₹· (6000 × 600)/900
= 4000.
∴ Hence, the capital of Rahul = 4000.
Question 2. The ratio of capitals of three persons is 3: 8: 5 and the profit of 1st person is 60 less of the 3rd person, calculate the total profit in this business.
Solution:
Given:
The ratio of capitals of three persons is 3: 8: 5 and the profit of 1st person is 60 less of the 3rd person
The ratio of the capitals of three persons
∴ The ratio of their profit is 3: 8:5
Let the profit of 1st and 3rd persons be ₹ 3x and ₹ 5x As per question, 5x – 3x = 60
⇒ 2x = 60
⇒ x = 30
∴ Profit of the first friend = ₹3x = ₹ 3 x 30 = ₹ 90
Profit of the second friend = ₹ 8x = ₹ 8 x 30 = ₹ 240
Profit of the third friend = ₹ 5x = ₹ 5 x 30 = ₹ 150
Hence, the total profit = (90+240 + 150) = 480.
“Understanding partnership business in Class 10 Maths”
Question 3. Jayanta, Ajit and Kunal started a partnership business investing₹15000. At the end of the year, Jayanta, Ajit and Kunal received ₹800, ₹1000 and 1200 respectively as profit share. Calculate the amount of Jayanta’s capital that was invested in the business.
Solution
Given:
Jayanta, Ajit and Kunal started a partnership business investing₹15000. At the end of the year, Jayanta, Ajit and Kunal received ₹800, ₹1000 and 1200 respectively as profit share.
Ratio of Jayanta, Ajit and Kunal’s profit Ratio of their capitals 800: 1000: 1200 = 4: 5: 6.
∴ Ratio of their capitals = 4 : 5 : 6
So, the part of Jayanta’s capital = \(\frac{4}{4+5+6}=\frac{4}{15}\)
∴ In ₹ 15000, Jayanta’s capital = ₹ \(15000 \times \frac{4}{5}=₹ 12000\)
Hence, in the business Jayanta invested ₹ 12000.
Question 4. If in partnership business the ratio of capitals of Rahul and Amit is 4: 5. Keeping 10% of the total profit in the business as the capital, the rest of the profit is distributed between Rahul and Amit. If thus the profit of Rahul be₹ 16000, then find the total profit of the business.
Solution:
Given:
If in partnership business the ratio of capitals of Rahul and Amit is 4: 5. Keeping 10% of the total profit in the business as the capital, the rest of the profit is distributed between Rahul and Amit. If thus the profit of Rahul be₹ 16000
Let the total profit be ₹ x
As per question, kept capital = ₹ x x(10/100)
= ₹( x/10)
∴ The distributed profit = \(₹\left(x-\frac{x}{10}\right)=₹ \frac{9 x}{10}\)
Now, ratio of the capitals of Rahul and Amit = 4:5
∴ The profit of Rahul = ₹ \(\frac{9 x}{10} \times \frac{4}{4+5}=₹ \frac{4 x}{10}\)
As per question, \(\text { (4) } 16000 \Rightarrow x=\frac{16000 \times 10}{4} \Rightarrow x=40000 .\)
Hence, the total profit = ₹ 40000.
“Class 10 Maths solved problems on partnership”
Question 5. In a partnership business the ratio of the capitals of three friends is 3 4 5. In the next year, if their capitals be increased by 10%, 15% and 20% respectively, then at the end of the second year at what ratio should their profits be distributed?
Solution
Given:
In a partnership business the ratio of the capitals of three friends is 3 4 5. In the next year, if their capitals be increased by 10%, 15% and 20% respectively,
Let the capitals of three friends be 3x, 4x and ₹ 5x.
So, at the end of the second year, the ratio of their capitals will be
\(\left(3 x+3 x \times \frac{10}{100}\right):\left(4 x+4 x \times \frac{15}{100}\right):\left(5 x+5 x \times \frac{20}{100}\right)\)= \(\frac{33 x}{10}: \frac{23 x}{5}: 6 x=33: 46: 60\)
Hence, the required ratio of the profit = 33 46 60.
Question 6. In a partnership business the ratio of capitals of Sujoy and Palash is 4 5 and the ratio of their profits is 2 3. If Sujoy has invested for 10 months then for how many months did Palash invest his capital?
Solution
Given:
In a partnership business the ratio of capitals of Sujoy and Palash is 4 5 and the ratio of their profits is 2 3.
Let the capitals of Sujoy and Palash be ₹ 4x and ₹ 5x
Also, let Palash invested for y months.
As per question, (4x × 10) (5x × y) =2 : 3
(40x / 5xy ) = 2/3 2y = 24 = y = 12
Hence, Palash invested for 12 months or 1 year.
Question 7. In a business, A invested 2 times capital than B and for a period of time which is also 3 times than B. If B gets 12000 from the profit, then what is the total profit ?
Solution
Given:
In a business, A invested 2 times capital than B and for a period of time which is also 3 times than B. If B gets 12000 from the profit
Let B invested x for y years.
So, the capital of A = ₹2x and time = 3y years.
∴ The ratio of their profit is (2x x 3y) : xy
= \(\frac{6 x y}{x y}=\frac{6}{1}\)
= 6 : 1.
Let the total profit = ₹ P
∴ The profit of B = \(₹ P \times \frac{1}{6+1}=₹ \frac{P}{7}\)
As per question, =12000 ⇒ P = 84000
Hence, the required total profit = 84000.
“WBBSE Class 10 Maths partnership example problems”
Question 8. In the year 2015, A invested ₹ 800 on 1st January, B invested ₹ 600 on 1st May and C invested 500 on 1st July. If the total profit of that year be ₹ 3480, find the profit of each of them.
Solution
Given:
In the year 2015, A invested ₹ 800 on 1st January, B invested ₹ 600 on 1st May and C invested 500 on 1st July.
Here, the capital of A was invested for 12 months, the capital of B was invested for 8 months and the capital of C was invested for 6 months.
∴ The ratio of (the capital of A) (the capital of B) (the capital of C)
= 800 x 12 : 600 x 8 : 500 x 6
= 16 : 8 : 5
So, from ₹3480, A will let profit ₹ \(3480 \times \frac{16}{16+8+5}\)
= ₹ \(3480 \times \frac{16}{29}=₹ 1\)
From ₹3480, B will get profit ₹ \(3480 \times \frac{8}{29}=₹ 960\)
From ₹3480, C will get profit ₹ \(3480 \times \frac{5}{29}=₹ 600\)
Hence, the profit of A, B and C will be ₹ 1920, ₹ 960, and ₹ 600, respectively.
Question 9. In a partnership business, Arpan invested ₹ 10000 for 6 months and Pulak invested some money for 8 months. If Pulak gets 4/9 part of the total profit, then find the capital of Pulak.
Solution: The part of profit of Pulak = \(\frac{4}{9}\)
∴ Part of profit of Arpan = \(\left(1-\frac{4}{9}\right)=\frac{5}{9}\)
Now, (Profit of Arpan) : (Profit of Pulak) = \(\frac{5}{9}: \frac{4}{9}=5: 4\)
Let the investment of Pulak be ₹ x
∴ 10000 x 6 : x : 8 = 5 : 4
⇒ \(\frac{10000 \times 6}{(x \times 8)}=\frac{5}{4}\)
⇒ 5 x x x 8 = 10000 x 6 x 4
⇒ \(x=\frac{10000 \times 6 \times 4}{5 \times 8}\)
⇒ x = 6000
Hence, Pulak invested ₹6000, for 8 months.
Question 10. In a partnership business, 6 times of the capital of A, 8 times of the capital of B and 10 times of the capital of C are equal. Then find the ratio of the capitals of A, B and C.
Solution
Given:
In a partnership business, 6 times of the capital of A, 8 times of the capital of B and 10 times of the capital of C are equal.
As per the question,6 × capital of A
= 8 capital of B
= 10 capital of C = x (let)
⇒ capital of A = \(\frac{x}{6}\)
capital of B = \(\frac{x}{8}\); and
capital of C = \(\frac{x}{10}\)
∴ The ratio of the capitals of A, B and C
= \(\frac{x}{6}: \frac{x}{8} \in \frac{1}{10}=\frac{1}{6}: \frac{1}{8}: \frac{1}{10}=20: 15: 12\)
Hence, the required ratio = 20 : 15 : 12.
Chapter 3 Partnership Business Solved Example Problems Long-Answer Type Question
“Step-by-step solutions for partnership business Class 10”
Example. 1. In a partnership business, A and B have invested 600 and 750 respectively. If the loss after 1 year be 72, then find the loss of each of them.
Solution:
Given:
In a partnership business, A and B have invested 600 and 750 respectively.
The proportion of capitals of A and B is 600: 750 = 4: 5.
∴ part of A’s loss = \(\frac{4}{4+5}=\frac{4}{9}\)
and part of B’s loss = \(\frac{5}{4+5}=\frac{5}{9}\)
So that A’s share of loss = ₹ \(72 \times \frac{4}{9}=₹ 32\)
and B’s share of loss = ₹ \(72 \times \frac{5}{9}=₹ 40\)
Hence, share of A’s and B’s loss are ₹32 and ₹40 respectively.
Example. 2. A started a business investing 1400. After 5 months, B joined the business and after 2 months more, C had joined the business. If their proportion of profits after one year be 43 2, then what amount of capitals had B and C invested in the business?
Solution: The proportion of profits of A, B and C = 4 : 3 : 2
∴ The proportion of their capital = 4 : 3 : 2
∴ part of A’s profit = \(\frac{4}{4+3+2}=\frac{4}{9}\)
part of B’s profit = \(\frac{3}{4+3+2}=\frac{3}{9}=\frac{1}{3}\)
part of C’s profit = \(\frac{2}{4+3+2}=\frac{2}{9}\)
Now, A’s capital in respect of 1 month = ₹(1400 x 12) = ₹ 16800
∴ \(\frac{4}{9}\) part of the capital = ₹ 16800
∴ \(\frac{1}{3},,,,,=₹ 16800 \times \frac{9}{4} \times \frac{1}{3}=12600 .\)
∴ \(\frac{2}{9},,,,=₹ 16800 \times \frac{9}{4} \times \frac{2}{9}=₹ 8400 .\)
But B and C had invested capitals for 7 months and 5 months respectively.
∴ Capital of B = ₹ 12600 ÷ 7 = ₹ 1800.
Capital of C = ₹ 8400 ÷ 5 = ₹ 1680.
B and C had invested =1800 and 1680 respectively in the business.
Example. 3. Sova and Sujit together after buying a car for 250000, sold it at ₹262500. If while buying the car, Sova gave money times of the money of Sujit, then find the part of the profit of each of them.
Solution: Let the capital of Sujit be ₹ x.
∴ The capital of Sova is \(₹ \mathrm{x} \times 1 \frac{1}{2}=₹ \frac{3 x}{2}\)
∴ Capital of Sova : Capital of Sujit = ₹ \(\frac{3 x}{2}\): ₹ x=3: 2
The S.P. (selling price) of the car = ₹ 262500
and the C.P. (cost price) of the car = ₹ 250000
∴ Net profit = ₹ (262500 – 250000) = ₹ 12500
∴ Sova’s profit = \(₹ 12500 \times \frac{3}{3+2}=₹ 12500 \times \frac{3}{5}=₹ 7500\)
Sujit’s profit = \(₹ 12500 \times \frac{2}{3+2}=₹ 12500 \times \frac{2}{5}=₹ 5000 .\)
Hence, Sova will get profit ₹ 7500 and Sujit will get profit ₹ 5000.
Example 4. Three friends, collecting ₹8000, 10000 and from the bank, started a business. At the end of the year, their profit is 13400. From that profit, they repaid the bank instalment of 5000 and then the rest of the profit was distributed amongst themselves according to the ratio of their capitals. Find the amount of profit of each of them.
Solution:
Given:
Three friends, collecting ₹8000, 10000 and from the bank, started a business. At the end of the year, their profit is 13400. From that profit, they repaid the bank instalment of 5000 and then the rest of the profit was distributed amongst themselves according to the ratio of their capitals.
The ratio of the capitals of three friends = 8000: 10000:12000 = 4:5:6.
∴ Part of the profit of the first friend = \(\frac{4}{4+5+6}=\frac{4}{15}\)
Part of the profit of the second friend = \(\frac{5}{4+5+6}=\frac{5}{15}=\frac{1}{3}\)
Part of the profit of the third friend = \(\frac{6}{4+5+6}=\frac{6}{15}\)
The gross profit of the business = ₹13400.
Instalment of the bank = ₹5000.
∴ Rest of the profit = ₹(13400 – 5000) = ₹ 8400.
∴ The first friend will get profit = \(₹ 8400 \times \frac{4}{15}=₹ 2240 .\)
The second friend will get profit = \(₹ 8400 \times \frac{1}{3}=₹ 2800 .\)
The third friend will get profit = \(₹ 8400 \times \frac{6}{15}=₹ 3360 .\)
Hence, the profits of the three friends are ₹ 2240, ₹ 2800 and ₹ 3360 respectively.
Example 5. At the beginning of a year, Pradipbabu and Pramiladebi started jointly a business investing 24000 and 30000 respectively. After 5 months Pradipbabu invested 4000 more in the business. If after the end of the year, the profit of the business be 27716, then find the amount of profit got by each of them.
Solution:
Given:
At the beginning of a year, Pradipbabu and Pramiladebi started jointly a business investing 24000 and 30000 respectively. After 5 months Pradipbabu invested 4000 more in the business. If after the end of the year, the profit of the business be 27716,
The capital of Pradipbabu with respect of 1 month
= ₹ {24000×5+ (24000 + 4000) × (12− 5)}
= ₹ 316000.
=The capital of Pramiladebi with respect of 1 month ₹ 30000 × 12 = ₹ 360000
Therefore, (capital of Pradipbabu) (capital of Pramiladebi) = 316000: 360000 = 79: 90
∴ Part of the capital of Pradipbabu = \(\frac{79}{79+90}=\frac{79}{169}\)
and part of the capital of Pramiladebi = \(\frac{90}{79+90}=\frac{90}{169}\)
∴ In ₹27716, Pradipbabu will get profit \(₹ 27716 \times \frac{79}{169}=₹ 12956\)
In ₹27716, Pramiladebi will get profit \(₹ 27716 \times \frac{90}{169}=₹ 14760\)
Hence, Pradipbabu and Pramiladebi will get profits of ₹ 12956 and ₹ 14760 respectively.
Example 6. At the beginning of a year, Arun and Ajoy jointly started a business investing 24000 and 30000 respectively. But after few months Arun invested 12000 more in the business. If the profit of the business be 14030 at the end of the year and Arun got7130 as the profit, then find the number of month after which Arun had invested more in the business.
Solution:
Given:
At the beginning of a year, Arun and Ajoy jointly started a business investing 24000 and 30000 respectively. But after few months Arun invested 12000 more in the business. If the profit of the business be 14030 at the end of the year and Arun got7130 as the profit,
Let Arun invested 12000 more after x months.
So, the capital of Arun with respect of 1 month
= ₹{24000 x x + (24000 + 12000)(12 – x)}
= ₹(24000x + 432000 – 36000x)
= ₹(432000 – 12000x)
= ₹{12000(36 – x)}.
Also, the capital of Ajoy with respect of 1 month = ₹30000 x 12 = ₹360000.
Total profit = ₹14030
Arun’s = ₹7130
∴ Ajoy’s = ₹(14030 – 7130) = ₹6900.
Now, (Arun’s profit) : (Ajoy’s profit) = 7130 : 6900 = 31 : 30.
We know that ratio of capital = ratio of profit
so, 12000(36 – x) : 360000 = 31 : 30
⇒ \(\frac{12000(36-x)}{360000}=\frac{31}{30}\)
⇒ \(\frac{36-x}{30}=\frac{31}{30}\)
⇒ 36 – x = 31
⇒ x = 36 – 31
⇒ x = 5.
Hence, Arun had invested ₹ 12000 more after 5 months of the starting of the business.
Example 7. Three friends A, B and C profited 1000. The ratio of capital of A and B is 2 3 and that of B and C is 2 5. Calculate the profit of each of them.
Solution:
(Capital of A) : (Capital of B) = 2 : 3 = 4 : 6
Also, (capital of B) : (capital of C) = 2 : 5 = 6 : 15
∴ Capital of A : Capital of B : Capital of C = 4 : 6 : 15
∴ Part of capital of A = \(\frac{4}{4+6+15}=\frac{4}{25}\)
Part of capital of B = \(\frac{6}{25}\)
Part of capital of C = \(\frac{15}{25}\)
So, from ₹ 1000, A will get \(₹ 1000 \times \frac{4}{25}=₹ 160\)
from ₹ 1000, B will get
\(₹ 1000 \times \frac{6}{25}=₹ 240\) and from ₹1000, C will get \(₹ 1000 \times \frac{15}{25}=₹ 600\)
Hence, the profit of A, B and C are ₹ 160 ₹ 240 and ₹ 600 respectively.
Example 8. At the beginning of a year, A, B and C jointly started a business. A invested 1/3 part of the capital and B invested an amount equal to the total capital of A and C. If the profit be at the end of the year, then find the profits of each of them.
Solution:
Let the capital be ₹ x
So, A invested ₹ \(\frac{x}{3}\) and the investment of B and C is \(₹\left(x-\frac{x}{3}\right)=₹ \frac{2 x}{3}\)
As per question, the investment of B = ₹\(\frac{x}{3}\) + investment of C
⇒ (Capital of B) – (Capital of C) = \(₹\frac{x}{3}\)
Now, adding (1) and (2) we get, 2 x (Capital of B) = \(₹\left(\frac{2 x}{3}+\frac{x}{3}\right)=₹ x\)
∴ Capital of B = ₹\frac{x}{2}
∴ From (1) we get capital of C = \(₹\left(\frac{2 x}{3}-\frac{x}{2}\right)=₹ \frac{x}{6}\)
So, (capital of A) : (capital of B) : (capital of C)
= \(\frac{x}{3}: \frac{x}{2}: \frac{x}{6}=\frac{1}{3}: \frac{1}{2}: \frac{1}{6}=2: 3: 1\)
∴ The part of the capital of A = \(\frac{2}{2+3+1}=\frac{2}{6}\)
The part of the capital of B = \(\frac{3}{6}\) and the part of the capital of C = \(\frac{1}{6}\) So, form ₹840, A will get ₹ 840 x \(\frac{2}{6}\) = ₹280
B will get ₹840 x \(\frac{3}{6}\) = ₹420 and C will get \(₹ 840 \times \frac{1}{6}=₹ 140\)
Hence, the profits of A, B and C are ₹280, ₹420 and ₹140 respectively.
Example 9. The ratio of the capitals of A, B and C is(1/2):(1/3):(1/4) in a partnership business. After 4 months, A have withdrawn half of his capital and after 8 months more, the profit of the business is 2024. Find the profit of A.
Solution:
The ratio of the capital of A, B and C = \(\frac{1}{2}: \frac{1}{3}: \frac{1}{4}=6: 4: 3\)
Let the capitals of A, B and C be₹6x, ₹4x and ₹3x respectively.
∴ With respect of 1 month, the capital of
A = \(₹\left(6 x \times 4+\frac{6 x}{2} \times 8\right)=₹(24 x+24 x)=₹ 48 x\)
With respect of 1 month, the capital of B = ₹4x x 12 = ₹48x
and with respect of 1 month, the capital of C = ₹3x x 12 = ₹36x
So, the ratio of the capitals of A, B and C = 48x : 48x : 36x = 4 : 4 : 3
∴ Part of the profit of A = \(\frac{4}{4+4+3}=\frac{4}{11}\)
∴ From ₹ 2024, A will get the profit of \(₹ 2024 \times \frac{4}{11}=₹ 736\)
Hence, A will get the profit ₹736.
Example 10. In a partnership business of Avoy and Pradip, the capital of Avoy is ₹ 23250. After 4 months, Avoy invested 3750 more and after 7 months, Pradip have withdrawn ₹ 3000 from the business. After one year, if the profits obtained by each of them be equal, then what amount of money had pradip invested at first in the business?
Solution:
Capital of Avoy with respect of 1 month
= ₹{23250 x 4 + (23250 + 3750) x 8} = ₹ 309000
Since the profits of both Avoy and Pradip are equal, so with respect of 1 month Avoy’s capital is equal to Pradip’s capital.
If Pradip would not withdraw ₹ 3000 after 7 months the capital of him would be ₹ 3000 x 5 = ₹ 14000
Then the capital of Pradip in 1 year would be ₹(309000 + 15000) = ₹324000.
∴ Capital of Pradip in 1 month = \(₹ \frac{32400}{12}=₹ 27000\)
Hence, Pradip had invested ₹27000 at first.