## Chapter 3 Partnership Business Solved Example Problems

**What is a 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**

**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.

**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.

**Class 10 Maths Solutions Wbbse**

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**

The total amount of capital is either collected equally from the partners or at a definite proportion decided unanimously on the before.**Capital**

**Profit Or Loss Distribution**

(a) May be distributed equally;

**(b) May be distributed according to their corresponding proportion of capitals, or**

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.**(c) May be distributed according to any other contact taken unanimously earlier.**

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.**Yearly Or Half-Yearly Allowance**

**Class 10 Maths Solutions Wbbse**

## Chapter 3 Partnership Business Solved Example Problems Ex. 1. Very Short-Answer Type Questions

**Multiple Choice Questions (MCQ)**

**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 Sumita’s profit Shreya’s profit Smita’s profit**

**= 50: 100: 150**

**= 1: 2: 3**

**(c) is correct.**

Smita invested in this business is 3000

**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.

(a) is correct.

The capital of Bimal in the business is 1500.

**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**

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.

**Class 10 Maths Solutions Wbbse**

**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

(Amal’s investment period) (Palash’s investment period)=1/2 :1/3= 3:2

**Maths Solutions Class 10 Wbbse**

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

**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** Let capital of C be x.

**Maths Solutions Class 10 Wbbse**

∴ 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.

**Class 10 Maths Solutions Wbbse**

## Chapter 3 Partnership Business Solved Example Problems Ex. 2. Short Answer Type Questions

**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.

**Wbbse Class 10 Maths Solutions**

**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

Hence, the total profit = (90+240 + 150) = 480.

**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.

**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)**

**Maths Solutions Class 10 Wbbse**

**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

Hence, the required ratio of the profit = 33 46 60.

**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.

**Maths Solutions Class 10 Wbbse**

**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.

As per question, =12000 ⇒ P = 84000

Hence, the required total profit = 84000.

**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)

Hence, the profit of A, B and C will be ₹ 1920, ₹ 960, and ₹ 600, respectively.

**Wbbse Class 10 Maths Solutions**

**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.**

**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)

## Chapter 3 Partnership Business Solved Example Problems Long-Answer Type Question

**Maths Solutions Class 10 Wbbse**

**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.

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?**

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.**

**Example. 4. Deepu, Rabeya and Megha started a small business with capital₹ 6500, ₹ 5200 and rd of that profit 9100 respectively and got a profit of₹ 14400 after 1 year. They have taken distributing equally within themselves and the rest of the profit according to the ratio of their capital. Find the parts of profits of each of them.**

Solution

**Given:**

Deepu, Rabeya and Megha started a small business with capital₹ 6500, ₹ 5200 and rd of that profit 9100 respectively and got a profit of₹ 14400 after 1 year. They have taken distributing equally within themselves and the rest of the profit according to the ratio of their capital.

The ratio of capitals of Deepu, Rabeya and Megha

=6500 : 5200: 9100

= 5: 4: 7.

**Maths Solutions Class 10 Wbbse**

Total profit of Megha Hence, Deepu, Rabeya and Megha will get profits 4700, 4400 and 5300 respectively.

**Example. 5. 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.

**Hence, the profits of the three friends are ₹ 2240, ₹ 2800 and ₹ 3360 respectively.**

**Example. 6. Three friends, investing ₹ 120000, 150000 and ₹ 110000, bought a bus. One friend 25 is a driver and the rest two friends are conductors. They decided that th of the gain will be distributed amongst themselves at the ratio of 3 2 2 due to their corresponding works and the rest at the ratio of their respective capitals. If the profit of a month be ₹ 29260, then find the amount of profit of each of them.**

**Wbbse Class 10 Maths Solutions**

**Given:**

Three friends, investing ₹ 120000, 150000 and ₹ 110000, bought a bus. One friend 25 is a driver and the rest two friends are conductors. They decided that th of the gain will be distributed amongst themselves at the ratio of 3 2 2 due to their corresponding works and the rest at the ratio of their respective capitals. If the profit of a month be ₹ 29260

The ratio of capitals of three friends 120000:150000:110000 = 12:15:11

**Example. 7. 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

**Hence, Pradipbabu and Pramiladebi will get profits of ₹ 12956 and ₹ 14760 respectively.**

**Example. 8. Rambabu and Karabi-didi jointly started a business investing₹ 30000 and 50000. After 6 months, Rambabu invested 40000 more in the business, but Karabi-didi had withdrawn 10000 for her own necessary. At the end of the year, if the profit of the business be ₹ 19000, then find the profit of each of them.**

**Solution:**

**Given:**

Rambabu and Karabi-didi jointly started a business investing₹ 30000 and 50000. After 6 months, Rambabu invested 40000 more in the business, but Karabi-didi had withdrawn 10000 for her own necessary. At the end of the year, if the profit of the business be ₹ 19000,

Hence, the profits of Rambabu and Karabi-didi are **₹ 10000 and ₹ 9000 respectively.**

**Example. 9. 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.**

**Class 10 Maths Wbbse Solutions**

**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

Hence, Arun had invested ₹ 12000 more after 5 months of the starting of the business.

**Example. 10. Three potters from Kumartuli collectively took a loan of ₹100000 from a Co- operative Bank to set up a modelling workshop. They made a contract that after paying back the annual bank instalment of 28100, they would divide half of the profit among themselves in terms of the number of working days and the other half will be equally divided among them. Last year they worked 300 days, 275 days and 350 days respectively and made a profit of 139100. Calculate the share of each in this profit.**

**Solution:**

**Given:**

Three potters from Kumartuli collectively took a loan of ₹100000 from a Co- operative Bank to set up a modelling workshop. They made a contract that after paying back the annual bank instalment of 28100, they would divide half of the profit among themselves in terms of the number of working days and the other half will be equally divided among them. Last year they worked 300 days, 275 days and 350 days respectively and made a profit of 139100.

Total profit = 139100

Instalment of the bank = 28100

**Wbbse Class 10 Maths Solutions**

**Example. 11. Two friends invested 40000 and 50000 respectively to start a business. They made a contract that they would divide 50% of the profit equally between themselves and the remaining profit in the ratio of their capitals. Calculate the share of profit of the first friend if it is ₹ 800 less than that of the second friend.**

**Solution:**

**Given:**

Two friends invested 40000 and 50000 respectively to start a business. They made a contract that they would divide 50% of the profit equally between themselves and the remaining profit in the ratio of their capitals.

The ratio of capitals of the two friends

= 40000 : 50000 = 4 : 5

**Hence, the profit of the first friend will be ₹ 6800.**

**Class 10 Maths Wbbse Solutions**

**Example. 12. Ashis and Sukamal invested ₹ 240000 and ₹ 300000 respectively at the beginning of the year to purchase a mini bus to run it on a route. After 4 months, their friend Anil joined them with a capital of 81000. Ashis and Sukamal have withdrawn that money in the ratio of their capitals. Calculate the share of each if they make a profit of 39150 at the end of the year.**

Solution:

**Given:**

Ashis and Sukamal invested ₹ 240000 and ₹ 300000 respectively at the beginning of the year to purchase a mini bus to run it on a route. After 4 months, their friend Anil joined them with a capital of 81000. Ashis and Sukamal have withdrawn that money in the ratio of their capitals.

Ratio of capitals of Ashis and Sukamal 240000:300000 = 4:5

**Hence, the profit of Ashis, Sukamal and Anil is ₹ 15660, ₹ 19575 and ₹ 3915 respectively.**

**Example. 13. Arun and Barun jointly started a business with capital 3000 and 5000 respectively. After 6 months, Arun invested 4000 more in the business, but Barun has withdrawn 1000 after 6 months from the business. If the profit in 1 year be₹ 6175, then find the profit of each of them.**

**Example. 14 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.**

**Hence, the profit of A, B and C are ₹ 160 ₹ 240 and ₹ 600 respectively.**

**Example. 15. A, B and C invested ₹ 5000, ₹ 6000 and ₹ 4000 respectively in a business. A has taken 30% of the profit so as to manage the business and the rest of the profit is distributed among them in accordance with the ratio of their capital. If after 1 year A has got 200 more than the aggregate of the profits of B and C, then calculate the profits of each of them and the total amount of profit.**

**Class 10 Maths Wbbse Solutions**

**Hence, the total profit is ₹ 3000 and the shares of A, B and C are ₹ 1600 ₹ 840 and ₹ 560 respectively.**

**Example. 16 Three friends invested ₹14000 in a business. One year hence, the profits of the first, the second and the third friends are ₹ 337-50, 1125 and 637-50 respectively. Find the amount of money invested by each of them.**

**Class 10 Maths Wbbse Solutions**

**Example. 17 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.**

**Example. 18 A, B and C invested 1100, 1300 and 1700 in a partnership business. After few month, 500 more is required in the business which B gave. If the profit after 1 year be₹2527 and the profit of A be ₹ 627, then after how many months, had B invested the excess money? Solution Let B had invested the excess money after x months**

**Example. 19** **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.**

**Class 10 Maths Wbbse Solutions**

**Example. 20. In a partnership business, Amal invested ₹ 600 more than Bimal. Bimal invested for months and Amal invested for 2 months more than Bimal. Now, if the profit of the business be 620 and Bimal got 140 less than Amal, find the capitals of Amal and Bimal.**

**Example. 21. 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?**