The Partnership topic in Quantitative Aptitude is a fundamental concept tested in several competitive exams like SSC, Banking, RRB, and State-level recruitment tests. It evaluates your understanding of profit-sharing based on capital and time investments. In this blog, we have provided the details about what Partnership means, its types, formulas, solved questions from recent exams, and key tricks to solve problems faster.
What Is Partnership in Quantitative Aptitude?
In Quantitative Aptitude, Partnership refers to the business relationship where two or more individuals invest money (capital) in a venture and share the profits or losses in a specified ratio.
Why is it asked in exams?
Partnership questions test your ability to calculate profit sharing, adjust for time-based investments, and apply ratios and proportions.
Skills required:
- Ratio and proportion handling
- Time-based logical adjustments
- Basic arithmetic
- Decision-making through elimination and approximation
Why Is Partnership Important in Competitive Exams?
Partnership problems are asked in exams because they test multi-step reasoning in a simple context.
| Exam | No. of Questions | Difficulty |
| SSC CGL / CHSL | 1–2 | Easy |
| IBPS PO / SBI PO | 1–2 | Moderate |
| RRB NTPC / Group D | 1 | Easy |
| State PSC / Police | 1–2 | Moderate |
Partnership Quantitative Aptitude Short Notes
Terms mostly used to solve Partnership questions are as follows:
| Term | Description |
| Partnership | Business venture by 2 or more individuals |
| Capital | Money invested by each partner |
| Time | Duration for which money is invested |
| Profit Sharing Ratio | Ratio of (Capital × Time) among partners |
| Working Partner | Actively manages the business |
| Sleeping Partner | Only invests money, does not take part in daily activities |
| Equal Time Investment | Share profit as per capital ratio only |
| Unequal Time Investment | Share profit as per (capital × time) ratio |
Quick Revision Summary of Partnership Based Questions
The core concepts used to solve most of the partnership questions are as follows:
| Concept | Explanation |
| Profit Sharing (Equal Time) | Profit ∝ Capital only |
| Profit Sharing (Unequal Time) | Profit ∝ Capital × Time |
| New Partner Entry | Recalculate total capital ratio from date of joining |
| Withdrawal or Exit | Adjust capital ratio based on remaining time |
| Total Profit Division | Total profit is divided in the final ratio of investments |
| Comparison Type Problems | Focus on capital ratios and investment duration |
What Are the Types of Partnership Questions in Quantitative Aptitude?
The Partnership section typically includes the following types of questions:
- Direct Questions: Based on static investments and equal time durations
- Time-Adjusted Questions: Capital invested for different time durations
- Change in Partnership: Partners join/leave at different points
- Profit Comparison: Comparing shares among multiple partners
- Combined Concept Questions: Involve ratios, averages, or percentages along with partnership
Partnership Formulas for Quantitative Aptitude
To solve Partnership questions faster, memorize and apply these key formulas:
- Equal Time Investment Profit Share Ratio=A:B=Capital of A:Capital of B\text{Profit Share Ratio} = A : B = \text{Capital of A} : \text{Capital of B}Profit Share Ratio=A:B=Capital of A:Capital of B
- Unequal Time Investment Profit Share Ratio=(Capital×Time)A:(Capital×Time)B\text{Profit Share Ratio} = (Capital \times Time)_A : (Capital \times Time)_BProfit Share Ratio=(Capital×Time)A:(Capital×Time)B
- Total Profit Division Individual Share=Individual RatioTotal Ratio×Total Profit\text{Individual Share} = \frac{\text{Individual Ratio}}{\text{Total Ratio}} \times \text{Total Profit}Individual Share=Total RatioIndividual Ratio×Total Profit
- If a Partner Enters Later
Adjust using time left till the end of the venture.
Partnership Tricks for SSC CGL and Other Exams
Tricks used to solve partnership questions are as follows:
- Multiply Capital × Time directly to get effective investment
- Assume total profit as 100 if not given helps in ratio problems
- Use options in reverse for fast elimination
- Keep units uniform months or years must be the same
- Practice time adjustment logic this is where most students go wrong
Solved Partnership Questions from 2024–25 Exams
Q1. (SSC CGL 2024 Tier 1 – Shift 2, Memory-Based)
A and B invested ₹12,000 and ₹16,000 respectively in a business. After 8 months, A withdrew his investment. At the end of the year, they earned a profit of ₹14,000. What is B’s share?
Solution:
Capital × Time:
A = 12000 × 8 = 96,000
B = 16000 × 12 = 1,92,000
Ratio = 96000:192000 = 1:2
B’s share = (2/3) × 14,000 = ₹9,333.33
Q2. (IBPS PO Prelims 2024 – Mock)
A, B, and C invested ₹10,000, ₹15,000, and ₹20,000 respectively. A invested for 12 months, B for 10 months, and C for 8 months. What is the ratio of their profit share?
Solution:
A = 10,000 × 12 = 1,20,000
B = 15,000 × 10 = 1,50,000
C = 20,000 × 8 = 1,60,000
Ratio = 120:150:160 = 4:5:5.33 ≈ 12:15:16
Q3. (RRB NTPC 2024 – Memory-Based)
If A and B share profits in 3:2 and A gets ₹6,000 more than B, what is the total profit?
Solution:
Let profit be 3x and 2x ⇒ Difference = x = ₹6,000
So, total = 5x = ₹30,000
Partnership Concepts for Bank Exams
In Bank exams like IBPS and SBI, Partnership questions may include additional logic layers such as coded values or profit–loss combined with investments.
Example:
A and B invested in the ratio 3:4, and their profits were in the ratio 6:8. Find who stayed longer and for how long.
You need to reverse-calculate time ratio assuming profit ∝ capital × time.
Common Mistakes to Avoid while Solving Partnership
While solving Partnership Quantitative Aptitude questions, avoid these common errors:
- Ignoring Time Factor: Always consider the time investment; don’t just compare capitals.
- Mismatched Units: Don’t mix months and years—standardize before calculation.
- Wrong Ratio Simplification: Carefully simplify ratios; one wrong step distorts the result.
- Assuming Equal Time: Only do so when clearly stated.
- Forgetting to Adjust for Entry/Exit: Recalculate ratios if partners join or leave mid-way.
FAQs
Use the direct formula: Profit ∝ Capital × Time. Skip long division by simplifying ratios.
Yes, especially in the Data Interpretation sets or standalone arithmetic questions.
Not recommended. It’s one of the easiest scoring topics.
Working partners manage the business; sleeping partners only invest money.
Ignoring the time factor when it differs for each partner.
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