Partnership Notes for SSC Exams

Partnership is a simple application of ratio and proportion in SSC Quantitative Aptitude. Two or more people invest money in a business and share the profit or loss. These partnership notes for SSC explain the sharing rule, the working and sleeping partner cases and the time-based sharing with solved examples.

Basic Rule of Partnership

• Profit or loss is divided in the ratio of Capital x Time of each partner.
• If the time is the same for all partners, profit is shared in the ratio of capitals.
• If the capital is the same, profit is shared in the ratio of time.
• A working partner manages the business and gets a salary or commission first.
• A sleeping partner only invests the money and takes no part in the work.

Important Formulas

Partners Joining or Leaving

When a partner joins later, count his time from the date he joined. If A invests Rs 8,000 for 12 months and B joins after 3 months with Rs 12,000, then B works for 9 months. The ratio is 8000 x 12 : 12000 x 9 = 96000 : 108000 = 8 : 9.

Fractional Investments

Sometimes the capital is given as fractions, such as A invests 1/2, B invests 1/3 and C invests 1/4. To find the ratio, take the LCM of the denominators (12) and multiply each fraction: 6 : 4 : 3. If the fractions are of the same total capital, you can also find the share of the rest.

Solved Examples

Example 1: A and B invest Rs 5,000 and Rs 7,000 respectively in a business. Their profit is Rs 6,000. Find the share of each.
Solution: Ratio = 5 : 7. A = 6000 x 5/12 = Rs 2,500. B = 6000 x 7/12 = Rs 3,500.

Example 2: A invests Rs 4,000 for 12 months and B invests Rs 6,000 for 8 months. Find the profit ratio.
Solution: A = 4000 x 12 = 48,000. B = 6000 x 8 = 48,000. Ratio = 1 : 1.

Example 3: A starts a business with Rs 8,000. After 3 months, B joins with Rs 12,000. Find the ratio of their profits at the end of the year.
Solution: A = 8000 x 12 = 96,000. B = 12000 x 9 = 108,000. Ratio = 96 : 108 = 8 : 9.

Example 4: A, B and C invest in the ratio 2 : 3 : 5. The total profit is Rs 15,000. Find C's share.
Solution: C = 15000 x 5/10 = Rs 7,500.

Example 5: A and B invest Rs 6,000 and Rs 4,000. A is a working partner and gets 10% of the profit as a salary. The profit is Rs 5,000. Find the share of each.
Solution: A's salary = Rs 500. Remaining profit = Rs 4,500, divided in the ratio 3 : 2. A = 500 + 2700 = Rs 3,200, B = Rs 1,800.

Example 6: A, B and C invest in the proportion 1/2 : 1/3 : 1/4. The profit is Rs 1,300. Find each share.
Solution: Ratio = 6 : 4 : 3 (total 13). Shares are Rs 600, Rs 400 and Rs 300.

Quick Tips to Solve Faster

• Always multiply capital by time before finding the ratio.
• Count the time of a late partner from the day he joined.
• Handle the commission or salary of a working partner before sharing the rest.
• Convert fractions of capital into whole numbers using the LCM.
• Cancel common factors in the ratio to make the division easy.

Common Mistakes to Avoid

• Using only the capital ratio when the times are different.
• Counting the full year for a partner who joined later.
• Dividing the profit equally when the capitals are different.
• Forgetting to deduct the salary of a working partner first.
• Mixing months and years in the same ratio.

Quick Revision Points

• Profit ratio = capital x time.
• Equal time: ratio of capitals.
• Working partner gets a share first, the rest is shared by capital x time.
• Late partner: count time from the date of joining.
• Convert fractional capitals to whole numbers using the LCM.

Practice Questions With Answers

1. A and B invest Rs 3,000 and Rs 5,000. The profit is Rs 4,000. How much does A get?
   Answer: Rs 1,500 (4000 x 3/8).
2. A invests Rs 2,000 for 6 months and B invests Rs 3,000 for 4 months. Find the profit ratio.
   Answer: 1 : 1 (12,000 : 12,000).
3. Three partners invest Rs 5,000, Rs 7,000 and Rs 8,000. The profit is Rs 10,000. Find B's share.
   Answer: Rs 3,500 (10000 x 7/20).
4. A invests Rs 6,000 and B joins after 6 months with Rs 6,000. Find the profit ratio at the end of the year.
   Answer: 2 : 1 (72,000 : 36,000).
5. A and B share profits in the ratio 3 : 2. The profit is Rs 5,000. How much does B get?
   Answer: Rs 2,000 (5000 x 2/5).
6. A invests Rs 4,000 for 12 months and B invests Rs 5,000 for 6 months. Find the profit ratio.
   Answer: 8 : 5 (48,000 : 30,000).
7. Capitals of A and B are in the ratio 5 : 3 and their times are in the ratio 2 : 3. Find the profit ratio.
   Answer: 10 : 9 (5 x 2 : 3 x 3).
8. A invests Rs 10,000 for 1 year and B invests Rs 20,000 for 6 months. Find the profit ratio.
   Answer: 1 : 1 (10,000 x 12 : 20,000 x 6).
9. The total profit is Rs 12,000. A and B share it in the ratio 7 : 5. How much does A get?
   Answer: Rs 7,000 (12000 x 7/12).
10. A invests 1/3 of the capital and B invests 1/4. The rest is invested by C. If the profit is Rs 1,200, find C's share.
    Answer: Rs 500 (C = 5/12 of the capital).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching SSC profit and loss practice paper to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Ratio and Proportion Notes
• Profit and Loss Notes
• Percentage Notes
• Mixture and Alligation Notes
• SSC Profit and Loss Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What is partnership in maths?

Partnership is a business in which two or more persons invest money together and share the profit or loss in an agreed ratio.

How many questions come from partnership in SSC exams?

Usually one question comes from partnership in some SSC Tier 1 papers.

On what basis is profit divided in a partnership?

Profit is divided in the ratio of capital multiplied by the time for which it was invested.

Who is a sleeping partner?

A sleeping partner only invests money and does not take part in running the business.

Who is a working partner?

A working partner manages the business and gets a salary or commission before the remaining profit is shared.

What if a partner joins late?

Count his investment only for the months he was in the business.

How do I handle fractional capitals?

Take the LCM of the denominators and convert the fractions into whole numbers.

How should I practise partnership?

Learn the rule, solve the examples here and then practise ratio and profit-loss sets.