Partnership in Quantitative Aptitude is an important arithmetic topic frequently asked in competitive exams like SSC, Banking, Railway, Defence, and various state-level exams. Questions from this chapter are logical, formula-based, and directly connected to Ratio and Proportion.
Many students find Partnership problems confusing at first because they involve profit sharing based on investment and time. However, once you understand the basic concept, Partnership in Quantitative Aptitude becomes one of the easiest scoring areas.
At Informosio, we believe in building strong mathematical foundations with step-by-step explanations and exam-focused strategies. In this complete guide, you will learn Partnership in Quantitative Aptitude with formulas, types, solved examples, shortcut tricks, and preparation tips.
What is Partnership?
Partnership is a business arrangement where two or more persons invest money in a business and share profit or loss according to their investment and time period.
In simple words:
Profit share ∝ Investment × Time
This is the most important concept in Partnership in Quantitative Aptitude.
Basic Formula of Partnership
If:
Person A invests ₹a for t₁ months
Person B invests ₹b for t₂ months
Then their profit ratio will be:
(a × t₁) : (b × t₂)
This formula is used in almost every Partnership in Quantitative Aptitude question.
Case 1: Investment for Same Time
If two partners invest different amounts for the same duration, profit is divided in ratio of their investments.
Example 1:
A invests ₹10,000
B invests ₹20,000
Business runs for 1 year
Profit ratio = 10,000 : 20,000
= 1 : 2
If total profit is ₹30,000:
A’s share = 10,000
B’s share = 20,000
Case 2: Same Investment, Different Time
If investment is same but time is different, profit is divided in ratio of time.
Example 2:
A invests ₹15,000 for 12 months
B invests ₹15,000 for 6 months
Profit ratio = 12 : 6
= 2 : 1
If total profit is ₹18,000:
A gets ₹12,000
B gets ₹6,000
Case 3: Different Investment and Different Time
This is the most common type in Partnership in Quantitative Aptitude.
Example 3:
A invests ₹10,000 for 12 months
B invests ₹20,000 for 6 months
Calculate investment × time:
A = 10,000 × 12 = 120,000
B = 20,000 × 6 = 120,000
Ratio = 120,000 : 120,000
= 1 : 1
Profit is shared equally.
Example 4 (Complete Problem)
A invests ₹5,000 for 12 months.
B joins after 4 months with ₹6,000.
Total profit = ₹8,800
Find B’s share.
Step 1: Calculate time period
A = 12 months
B = 8 months
Step 2: Multiply investment × time
A = 5,000 × 12 = 60,000
B = 6,000 × 8 = 48,000
Step 3: Ratio
60,000 : 48,000
= 5 : 4
Step 4: Profit division
Total parts = 9
B’s share = (4/9) × 8,800
= ₹3,911.11 (approx)
This is a standard question type in Partnership in Quantitative Aptitude.
Active and Sleeping Partner
In some questions, one partner works actively and receives salary before profit division.
Example:
A and B invest in ratio 3 : 2.
A gets ₹1,000 monthly salary.
Total annual profit = ₹60,000.
First deduct A’s salary:
₹1,000 × 12 = ₹12,000
Remaining profit = 48,000
Now divide in ratio 3 : 2.
This concept is also common in Partnership in Quantitative Aptitude.
Important Concepts to Remember
- Profit share depends on investment and time.
- Always convert months properly.
- Use LCM if required.
- Simplify ratio before solving.
- Carefully read joining and leaving conditions.
Shortcut Tips for Partnership
To solve Partnership in Quantitative Aptitude quickly:
- Directly multiply capital and time.
- Ignore zeros while forming ratio.
- Simplify before dividing profit.
- Use fraction method for faster calculation.
- Practice mixed time questions regularly.
Speed is very important in exams.
Common Mistakes Students Make
- Forgetting to calculate correct time.
- Not multiplying investment with time.
- Making calculation mistakes in ratio.
- Ignoring salary deduction.
- Dividing profit incorrectly.
Avoiding these mistakes improves accuracy.
Advanced Type: Partner Leaving
Sometimes a partner leaves before the year ends.
Example:
A invests ₹8,000 for 12 months.
B invests ₹12,000 but leaves after 6 months.
Total profit = ₹10,000.
Step 1:
A = 8,000 × 12 = 96,000
B = 12,000 × 6 = 72,000
Step 2:
Ratio = 96 : 72
= 4 : 3
Step 3:
Total parts = 7
B’s share = (3/7) × 10,000
= ₹4,285.71 (approx)
This is a high-probability question in Partnership in Quantitative Aptitude.
Why Partnership Is Important
Partnership is connected to:
- Ratio and Proportion
- Percentage
- Profit and Loss
- Simple Interest
- Time-based calculations
If your basics are strong, this chapter becomes very easy.
In SSC and Banking exams, usually 1–2 direct questions appear from Partnership in Quantitative Aptitude.
Practice Strategy
To master Partnership in Quantitative Aptitude:
- Solve 20 questions daily.
- Practice mixed time cases.
- Focus on word problems.
- Solve previous year questions.
- Attempt sectional mock tests.
Consistency builds speed.
Final Conclusion
Partnership in Quantitative Aptitude is a scoring and formula-based topic. Once you clearly understand the investment × time rule, most questions become straightforward.
At Informosio, we recommend focusing on concept clarity first and then practicing regularly to improve speed and accuracy. With consistent preparation and proper strategy, Partnership can become one of your strongest arithmetic chapters.
Master the basics, practice daily, and stay consistent — success will follow.
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