Partnership
⚡ Unlock time-saving calculation tricks and mental math techniques. Solve complex problems in seconds with proven shortcut methods used by top performers.
Shortcut Techniques
Study MaterialShortcut Techniques – Partnership
Shortcut techniques in Partnership help candidates solve aptitude questions quickly and accurately in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, and placement examinations.
Most partnership questions are based on:
- Capital investment
- Investment duration
- Profit-sharing ratios
- Admission of new partners
- Salary and commission adjustments
- Ratio-based calculations
Using shortcut techniques reduces lengthy calculations and improves problem-solving speed significantly.
Why Learn Partnership Shortcuts?
- Reduces calculation time in exams.
- Improves ratio calculation speed.
- Useful in Banking and SSC arithmetic.
- Helps solve complex investment problems quickly.
- Improves logical and analytical thinking.
Shortcut #1: Basic Partnership Rule
The most important rule in partnership is:
Profit ∝ Capital × Time
✔ Always multiply investment by time before forming ratios.
Shortcut #2: Same Time Investment Trick
If all partners invest for the same duration:
Profit Ratio = Investment Ratio
Example:
A invests 20000
B invests 30000
Same duration
Profit ratio:
= 2 : 3
Shortcut #3: Same Investment Trick
If all partners invest equal money:
Profit Ratio = Time Ratio
Example:
A invests for 12 months
B invests for 8 months
Profit ratio:
= 12 : 8
= 3 : 2
Shortcut #4: Direct Capital-Time Method
When capitals and time periods are different:
Profit Ratio = (Capital × Time)
Example:
A invests 10000 for 12 months
B invests 15000 for 8 months
Ratio:
= 10000 × 12 : 15000 × 8
= 120000 : 120000
= 1 : 1
Shortcut #5: Ignore Common Zeros
Remove common zeros while forming ratios.
10000 : 15000 = 10 : 15 = 2 : 3
✔ This saves calculation time in competitive exams.
Shortcut #6: Monthly Unit Method
Convert years into months to avoid confusion.
1 year = 12 months
Example:
2 years = 24 months
6 months remains unchanged
Shortcut #7: Profit Share Formula
If total profit is known:
Partner's Share = (Partner Ratio / Total Ratio) × Total Profit
Example:
Profit ratio = 2 : 3
Total profit = 25000
A's share:
= (2/5) × 25000
= 10000
Shortcut #8: New Partner Admission Trick
When a new partner joins later:
- Calculate remaining investment duration carefully.
- Use only active investment period.
Capital × Active Months
Example:
A invests 12000 for 12 months
B joins after 4 months with 15000
B's active period:
= 8 months
Ratio:
= 12000 × 12 : 15000 × 8
= 6 : 5
Shortcut #9: Salary Deduction Technique
If an active partner receives salary or commission:
Deduct salary first, then divide remaining profit.
Example:
Total profit = 50000
Manager salary = 10000
Remaining profit:
= 40000
Shortcut #10: Fraction Method for Quick Shares
Convert ratio into fraction form.
Share = Ratio Part / Total Parts
Example:
Ratio = 3 : 7
Total parts = 10
First share:
= 3/10
Shortcut #11: Equal Investment Shortcut
If profit shares are equal:
Capital × Time values are equal
Use this shortcut to find unknown investment or time quickly.
Shortcut #12: Ratio Simplification Trick
Always simplify profit ratios before final calculations.
120000 : 180000 = 2 : 3
✔ Simplified ratios make calculations much faster.
Shortcut #13: Quick Mental Multiplication
Use mental multiplication for capital-time products.
15000 × 8 = 15 × 8 = 120
Ignore common zeros during intermediate calculations.
Shortcut #14: Withdrawal and Additional Investment Trick
If a partner changes investment amount during the year:
- Break the investment into separate periods.
- Calculate capital × time separately.
- Add all contributions.
Example:
A invests:
10000 for first 6 months
15000 for next 6 months
Equivalent capital:
= (10000 × 6) + (15000 × 6)
Shortcut #15: Partnership Ratio Memory Table
| Condition | Profit Ratio |
|---|---|
| Same Time | Capital Ratio |
| Same Capital | Time Ratio |
| Different Capital & Time | Capital × Time |
Shortcut #16: Approximation Technique
In MCQs, approximate values whenever options are widely separated.
Example:
9999 × 12 ≈ 10000 × 12
= 120000
Shortcut #17: Partnership with Bonus Method
If one partner gets bonus:
- Deduct bonus first.
- Then divide remaining profit.
Total Profit − Bonus = Divisible Profit
Important Exam Tips
- Always use Capital × Time method.
- Convert years into months whenever necessary.
- Simplify ratios before calculations.
- Deduct salary or bonus before profit sharing.
- Practice new partner admission problems regularly.
- Use fraction methods for quick calculations.
- Verify final ratios carefully.
Shortcut techniques in Partnership help candidates improve calculation speed, reduce lengthy computations, and solve arithmetic aptitude questions efficiently in competitive examinations.