Hello Students,
I am Rahul Sir, an IIT-level Mathematics expert and aptitude trainer with years of experience guiding banking aspirants toward success in competitive examinations. Partnership is one of the most important topics in the Arithmetic Aptitude section of IBPS PO and IBPS Clerk exams. Questions from partnership are generally straightforward, scoring, and less time-consuming if you understand the concepts properly.
Partnership problems are based on the sharing of profits and losses among individuals who invest money in a business. The distribution depends on two factors: the amount invested and the duration for which the investment remains in the business. Most candidates make mistakes because they memorize formulas without understanding the logic behind investment-time relationships.
In banking examinations, partnership questions often appear in simplified arithmetic forms, making them excellent opportunities to score quickly. By mastering a few shortcuts and learning how to identify investment ratios, you can solve these questions within seconds.
In this article, I will explain important concepts, formulas, shortcuts, and examples that will help you tackle partnership questions confidently in IBPS PO and Clerk examinations.
1. Understanding the Basic Concept of Partnership
Partnership refers to a business arrangement where two or more individuals invest money together and share profits or losses according to their contribution. The contribution depends on both the capital invested and the duration for which the capital remains invested.
The fundamental principle is:
Profit Share ∝ Investment × Time
If two partners invest the same amount for the same duration, they share profits equally. However, if either the amount invested or the duration differs, profit distribution changes accordingly.
For example:
A invests ₹10,000 for 12 months.
B invests ₹20,000 for 12 months.
Ratio of investment:
10,000 : 20,000 = 1 : 2
Therefore profit ratio = 1 : 2
If total profit = ₹9,000
A’s share = ₹3,000
B’s share = ₹6,000
Most IBPS questions are based on this simple concept. Before applying shortcuts, always understand the relationship between capital and time.
2. The Golden Formula of Partnership
The most important formula in partnership is:
Profit Ratio = (Capital × Time) Ratio
Whenever capitals and durations differ, multiply both values and compare.
Example:
A invests ₹5,000 for 10 months.
B invests ₹8,000 for 5 months.
Investment-Time Product:
A = 5,000 × 10 = 50,000
B = 8,000 × 5 = 40,000
Profit Ratio:
50,000 : 40,000
5 : 4
Suppose profit = ₹18,000
A’s Share:
18000 × 5/9 = ₹10,000
B’s Share:
18000 × 4/9 = ₹8,000
This formula solves almost every partnership question in banking exams.
Students who master this concept rarely struggle with partnership problems.
3. Shortcut for Equal Time Investments
Many IBPS questions involve investments made for equal durations.
In such cases:
Profit Ratio = Capital Ratio
Example:
A invests ₹25,000
B invests ₹35,000
Both invest for one year.
Profit ratio:
25,000 : 35,000
5 : 7
Total profit = ₹24,000
A’s share:
24000 × 5/12 = ₹10,000
B’s share:
24000 × 7/12 = ₹14,000
Shortcut:
Ignore zeros and directly simplify the ratio.
This saves valuable time during examinations.
Whenever time remains equal, focus only on the capitals and avoid unnecessary calculations.
4. Shortcut for Equal Capital Investments
Sometimes all partners invest the same amount but for different durations.
Then:
Profit Ratio = Time Ratio
Example:
A invests ₹20,000 for 12 months.
B invests ₹20,000 for 8 months.
Ratio:
12 : 8
3 : 2
Profit = ₹15,000
A’s share:
15000 × 3/5 = ₹9,000
B’s share:
15000 × 2/5 = ₹6,000
Since capitals are identical, ignore them completely.
This shortcut reduces calculation time significantly and is frequently useful in clerk-level exams.
5. Handling Change in Capital During Business
Many questions involve additional investments after a few months.
Example:
A invests ₹20,000 for 12 months.
B invests ₹30,000 initially and withdraws after 6 months.
Calculation:
A = 20,000 × 12 = 240,000
B = 30,000 × 6 = 180,000
Ratio:
240,000 : 180,000
4 : 3
If profit = ₹14,000
A gets ₹8,000
B gets ₹6,000
Always divide the timeline carefully and calculate investment-month products separately.
This is one of the most common partnership question types in IBPS PO exams.
6. Working Partner Questions
A working partner contributes labor in addition to capital.
Usually, a fixed salary or commission is paid before profit distribution.
Example:
Profit = ₹50,000
Working partner salary = ₹5,000
Remaining profit = ₹45,000
Capital ratio:
2 : 3
Profit distribution:
A = 45,000 × 2/5 = ₹18,000
B = 45,000 × 3/5 = ₹27,000
Add salary if applicable.
Working partner receives:
₹27,000 + ₹5,000 = ₹32,000
Read questions carefully because candidates often forget salary adjustments.
7. Reverse Partnership Problems
Sometimes profit shares are given and capital must be found.
Example:
Profit ratio = 3 : 5
Investment durations are equal.
Capital ratio?
Since time is same:
Capital ratio = Profit ratio
= 3 : 5
If time differs, use:
Capital Ratio = Profit Ratio ÷ Time Ratio
These questions are common in IBPS mains examinations and require logical thinking instead of lengthy calculations.
8. Partnership with Three Partners
Questions involving three partners are common in banking exams.
Example:
A = ₹10,000 for 12 months
B = ₹15,000 for 12 months
C = ₹20,000 for 12 months
Ratio:
10 : 15 : 20
2 : 3 : 4
Profit = ₹45,000
A = ₹10,000
B = ₹15,000
C = ₹20,000
Always simplify the ratio first before distributing profit.
This minimizes calculation errors and improves speed.
9. Common Mistakes Students Make
Many students lose marks because of avoidable mistakes.
Common errors include:
- Ignoring investment duration.
- Forgetting withdrawals.
- Incorrect ratio simplification.
- Calculating profit before salary deduction.
- Using wrong profit-sharing formula.
- Mixing capital ratio with profit ratio.
To avoid mistakes:
- Write capital and time separately.
- Multiply systematically.
- Simplify ratios before calculations.
- Recheck the final distribution.
A disciplined approach can improve accuracy dramatically.
10. Exam-Oriented Tricks for Fast Solving
Important speed tricks:
- Cancel common zeros immediately.
- Simplify ratios at every step.
- Use fractions instead of decimals.
- Memorize ratio-to-share conversion.
- Practice mental multiplication.
- Identify whether time or capital is equal.
- Focus on investment-month products.
- Avoid unnecessary calculations.
- Use approximation where options permit.
- Solve at least 100 partnership questions before the exam.
Regular practice develops pattern recognition, allowing you to solve questions in under one minute.
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