Patwari Exam · Reasoning
Percentage & Number System
This note explains percentage formulas, LCM-HCF, and divisibility rules for quick problem solving.
- Reasoning & Numerical Ability
- 5 min read
Verified 6 October 2026
Key Formulas & Methods
- Percentage formula
- Percentage formula: (part/whole) × 100 = percentage.
- Increase/decrease formula
- Increase: new value = old × (1 + r/100); decrease: new value = old × (1 − r/100).
- Percentage change
- Percentage change: (new − old)/old × 100.
- Number types
- Types of numbers: natural (1,2,3…), whole (0,1,2…), integers (…−2,−1,0,1,2…), prime (2,3,5,7,11…).
- LCM × HCF rule
- LCM × HCF = number₁ × number₂.
- Divisibility rules
- Divisibility rules: by 2 → last digit even; by 3 → sum of digits divisible by 3; by 9 → sum of digits divisible by 9.
- Exam tip
- Exam tip: a% of b = b% of a — this trick gives a quick answer.
Frequently Asked Questions
What is the basic formula for finding a percentage?+
Percentage = (part/whole) × 100.
How do you find the new value after an increase or decrease?+
After an increase, new value = old × (1 + r/100), and after a decrease, new value = old × (1 − r/100).
What is the relationship between LCM and HCF?+
For any two numbers, LCM × HCF = number₁ × number₂; for divisibility, the last digit must be even for 2, while the sum of digits must be divisible by 3 or 9 respectively for those numbers.