Shortcut Techniques
Ratio and Proportion · Study material
Shortcut Techniques – Ratio and Proportion
Shortcut techniques in Ratio and Proportion help candidates solve aptitude questions quickly and accurately in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, and placement examinations.
Instead of lengthy calculations, these methods focus on:
- Fast ratio simplification
- Quick proportional calculations
- Direct and inverse variation shortcuts
- Fraction-based techniques
- Cross multiplication methods
- Partnership shortcuts
- Mental calculation tricks
Why Learn Ratio & Proportion Shortcuts?
- Improves speed in arithmetic calculations.
- Reduces lengthy proportional calculations.
- Useful in Time & Work and Partnership problems.
- Helps solve comparison questions quickly.
- Improves logical and analytical thinking.
Shortcut #1: Convert Ratio into Fraction
A ratio can always be converted into fraction form for easier comparison.
a : b = a/b
Example:
3 : 5
= 3/5
✔ Fraction form helps in quick comparison of ratios.
Shortcut #2: Simplify Ratios Quickly
Always divide both terms by their HCF.
Divide by HCF of both terms
Example:
24 : 36
HCF = 12
= 2 : 3
Shortcut #3: Comparison Using Cross Multiplication
To compare two ratios:
a : b and c : d
Compare:
ad and bc
Example:
Compare 5 : 8 and 7 : 10
5 × 10 = 50
8 × 7 = 56
Since 50 < 56
Therefore:
5 : 8 < 7 : 10
Shortcut #4: Direct Ratio Multiplication Trick
When all terms increase or decrease proportionally, multiply directly.
New Ratio = Old Ratio × Change Factor
Example:
Ratio = 2 : 3
Increase by 50%
= 2 × 1.5 : 3 × 1.5
= 3 : 4.5
Shortcut #5: Sum Method in Ratio Problems
If ratio is given:
a : b : c
Then total parts:
Total Parts = a + b + c
Example:
Ratio = 2 : 5 : 3
Total parts:
= 10
✔ Useful in money distribution and partnership questions.
Shortcut #6: Find Individual Share Quickly
If total amount is T:
Individual Share = (Ratio Part / Total Parts) × T
Example:
Ratio = 2 : 3
Total amount = 1000
First share:
= (2/5) × 1000
= 400
Shortcut #7: Proportion Cross Multiplication Trick
In proportion:
a : b :: c : d
Then:
ad = bc
Example:
2 : 5 :: x : 20
2 × 20 = 5x
x = 8
Shortcut #8: Direct Proportion Shortcut
If one quantity increases, the other also increases.
x/y = Constant
Example:
8 workers complete work in 12 days.
16 workers will complete in:
= 6 days
Shortcut #9: Inverse Proportion Shortcut
If one quantity increases, the other decreases.
x × y = Constant
Example:
5 workers complete work in 20 days.
10 workers complete in:
= (5 × 20)/10
= 10 days
Shortcut #10: Duplicate Ratio Trick
For square relationships:
Duplicate Ratio = Square of Ratio Terms
Example:
Ratio = 4 : 7
Duplicate ratio:
= 16 : 49
Shortcut #11: Compound Ratio Shortcut
Multiply antecedents together and consequents together.
(a : b) and (c : d)
Compound Ratio:
= ac : bd
Example:
2 : 5 and 3 : 7
Compound ratio:
= 6 : 35
Shortcut #12: Partnership Shortcut
Profit sharing in partnership:
Profit ∝ Investment × Time
Example:
A invests 10000 for 12 months.
B invests 15000 for 8 months.
Ratio:
= 10000 × 12 : 15000 × 8
= 1 : 1
Shortcut #13: Ratio Change Technique
When quantities increase or decrease:
New Ratio = Old Quantity ± Change
Example:
Ratio = 3 : 5
Add 2 to both:
= 5 : 7
Shortcut #14: LCM Method for Ratio Comparison
Convert ratios into equal denominators for fast comparison.
Equal denominator → Compare numerators
Example:
2/3 and 5/7
= 14/21 and 15/21
Therefore:
5/7 > 2/3
Shortcut #15: Unit Matching Rule
Always convert quantities into the same units before forming ratios.
✔ Incorrect units are one of the biggest causes of mistakes in ratio questions.
Example:
2 kg : 500 g
= 2000 : 500
= 4 : 1
Important Exam Tips
- Always simplify ratios completely.
- Convert quantities into same units before comparison.
- Use cross multiplication in proportion problems.
- Memorize duplicate and compound ratio concepts.
- Practice direct and inverse variation regularly.
- Use fraction methods for faster calculations.
- Verify calculations carefully in partnership questions.
Shortcut techniques in Ratio and Proportion help candidates improve speed, reduce calculation time, and solve aptitude questions efficiently in competitive examinations.