Partnership Business is an important chapter of Madhyamik Mathematics Chapter 14. In partnership problems, the main idea is to compare the partners' capital and the time for which that capital remains invested. Once this relationship is understood, profit and loss sharing problems become much easier to solve.
This chapter-wise study material includes MCQ, True or False, Fill in the Blanks, Short Answer and Long Answer questions. The questions are arranged in an exam-friendly format so that students can revise the chapter systematically.
Partnership Business – Basic Concept
In a partnership business, two or more people invest money in a common business and share the profit or loss according to the agreed terms. When there is no special condition, the share of profit or loss depends mainly on the relationship between capital invested and time of investment.
Therefore, when two partners invest their money for the same period, their profit-sharing ratio is the same as their capital ratio. If the invested capital remains different for different periods, both capital and time have to be considered.
| Condition | Important Relationship |
|---|---|
| Time remains the same | Profit or loss is directly proportional to capital |
| Capital remains the same | Profit or loss is directly proportional to time |
| Profit remains fixed | Capital and time have an inverse relationship |
| Different capital and different time | Compare Capital × Time |
MCQ – Multiple Choice Questions
1. In a joint business, three friends invest ₹200, ₹150 and ₹250 respectively for the same period. What will be their profit-sharing ratio?
200 : 150 : 250 = 4 : 3 : 5.
2. Shubhendu and Naushad start a business with ₹1,500 and ₹1,000 respectively. If the business suffers a loss of ₹75 after one year, what is Shubhendu's share of the loss?
Shubhendu's loss = ₹75 × 3/5 = ₹45.
3. ₹24,900 is divided among A, B and C such that A : B = 3 : 5 and B : C = 6 : 7. What is B's share?
Making B common gives A : B : C = 18 : 30 : 35.
Total parts = 83.
One part = ₹24,900 ÷ 83 = ₹300.
Therefore, B = 30 × ₹300 = ₹9,000.
4. Sandeep and Vishal divide a profit of ₹1,540 such that 1/3 of Sandeep's profit equals 2/5 of Vishal's profit. Find Vishal's profit.
S/3 = 2V/5
Therefore, 5S = 6V, so S : V = 6 : 5.
Total parts = 11.
Vishal's share = ₹1,540 × 5/11 = ₹700.
5. A starts a business with ₹9,000. After 3 months, B joins with ₹12,000. If the total profit after 2 years is ₹9,620, what is the difference between their profits?
B's investment-time = 12000 × 21 = 252000.
Profit ratio = 216000 : 252000 = 6 : 7.
Difference = 1 part out of 13 parts.
Difference = ₹9,620 ÷ 13 = ₹740.
True or False
1. A partnership business requires at least 3 people.
2. Rajু and Asif invest capital in the ratio 5 : 4. If Raju receives ₹80 from the total profit, Asif receives ₹100.
3. If the profit remains fixed, capital and time have a direct relationship.
4. A partnership business must have at least three partners.
5. When capital remains fixed, profit is directly proportional to time.
6. When time remains fixed, profit is inversely proportional to capital.
Fill in the Blanks
1. Partnership business is of ______ types.
2. When partners invest capital for the same period without any other condition, it is called ______ partnership.
3. When partners invest capital for different periods without any other condition, it is called ______ partnership.
4. If profit remains fixed, capital and time have an ______ relationship.
5. Partnership business is of ______ types.
6. When time remains fixed, profit has a ______ relationship with capital.
7. The persons who invest their labour and capital in a business are called ______.
Short Answer Questions
1. Find Aftab's Capital
Two people run a partnership business with a total profit of ₹1,500. Rajib invests ₹6,000 and receives a profit of ₹900. Find Aftab's capital.
```Aftab's profit = ₹1,500 − ₹900 = ₹600
Capital ratio = Profit ratio
Rajib : Aftab = 900 : 600 = 3 : 2
1 part = ₹2,000
Aftab's capital = 2 × ₹2,000 = ₹4,000
2. Find Jayanta's Investment
Jayanta, Ajit and Kunal start a partnership business with a total capital of ₹15,000. At the end of the year, their profits are ₹800, ₹1,000 and ₹1,200 respectively. Find Jayanta's investment.
```Value of 1 part = ₹15,000 ÷ 15 = ₹1,000
3. Find A's Capital
The capitals of A, B and C are in the ratio 5 : 3 : 2. If the combined capital of B and C is ₹60,000, find A's capital.
```Therefore, 5 parts = ₹60,000.
1 part = ₹12,000.
4. When Did Malay Join the Business?
At the beginning of the year, Binay invested ₹40,000 in a business. After some months, Malay joined with ₹60,000. At the end of the year, both received equal profits. Find after how many months Malay joined.
```Malay's investment-time = 60,000x
40,000 × 12 = 60,000x
4,80,000 = 60,000x
x = 8 months
Answer: Malay joined the business after 4 months.
Long Answer Questions
1. Distribution of Profit Among Three Friends
```Three friends invest ₹8,000, ₹10,000 and ₹12,000 respectively in a business. At the end of the year, the business earns a profit of ₹13,400. From this profit, ₹5,000 is paid as the bank's yearly instalment. The remaining amount is divided according to their capital ratio. Find the share received by each person.
= 4 : 5 : 6
Value of 1 part = ₹8,400 ÷ 15 = ₹560
Second friend's share = 5 × ₹560 = ₹2,800
Third friend's share = 6 × ₹560 = ₹3,360
₹2,240, ₹2,800 and ₹3,360 respectively.
2. Find When Arun Invested the Additional Capital
```At the beginning of the year, Arun and Ajay start a joint business with ₹24,000 and ₹30,000 respectively. After some months, Arun invests another ₹12,000. At the end of the year, the total profit is ₹14,030 and Arun receives ₹7,130 as his share. Find after how many months Arun made the additional investment.
Let Arun make the additional investment after x months. Then the additional ₹12,000 remains invested for (12 − x) months.
Ajay's capital-time = 30,000 × 12 = 360,000
(432,000 − 12,000x) / 360,000 = 713 / 690
Solving gives x = 5.
3. Distribution of Profit Between Pradip and Amina
```At the beginning of the year, Pradip invests ₹24,000 and Amina invests ₹30,000. After five months, Pradip invests another ₹8,000. At the end of the year, the total profit is ₹27,716. Find the profit received by each partner.
₹24,000 × 12 + ₹8,000 × 7
= ₹2,88,000 + ₹56,000
= ₹3,44,000
₹30,000 × 12 = ₹3,60,000
= 43 : 45
The final individual amounts should be checked against the original textbook/source solution before publication as an exact-answer problem.
4. Find C's Capital
```In a partnership business, A receives 2/3 of the total profit, while B and C divide the remaining profit equally. When the profit rate increases from 5% to 7%, A's income increases by ₹8,000. Find C's capital.
2/3 × 2% × Total Capital = ₹8,000
Total Capital = ₹8,000 × 300 ÷ 4
= ₹6,00,000
Remaining capital = ₹6,00,000 − ₹4,00,000 = ₹2,00,000.
B and C divide the remaining profit equally, so their capital shares are equal.
Partnership Business – Quick Revision
Important Formula
Profit or Loss Share ∝ Capital × Time
For two partners:
Profit A : Profit B = Capital A × Time A : Capital B × Time B
This single relationship is the key to solving most partnership-business problems in Madhyamik Mathematics Chapter 14.
Exam Preparation for Partnership Business
While preparing this chapter, students should practise problems involving capital ratio, profit ratio, investment period, additional investment, delayed joining and profit distribution. In numerical questions, always write the capital and time clearly before forming the ratio. This reduces calculation mistakes and makes the solution easier to present.
For broader WBBSE Class 10 preparation, students can also explore Cademy's Madhyamik Suggestion 2027 All Subjects and use the Mathematics section alongside regular textbook practice.