Arithmetic
Number System, Percentage, Ratio, Profit-Loss, Time-Work
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Overview
Arithmetic forms the quantitative backbone of the HTET reasoning section across all three levels (PRT, TGT, PGT). Questions typically test speed and accuracy rather than deep mathematical insight—examiners want to see if you can handle classroom-level calculations confidently.
This topic carries 5–8 questions on average. Mastery here directly boosts your score because these are often the most straightforward questions in the paper, provided you know the shortcuts. The concepts also overlap with the Mathematics subject paper for Level 1 and Level 2 candidates.
Focus areas: quick mental math for percentages, recognising standard ratio patterns, applying profit-loss formulas without confusion over cost vs selling price, and choosing the right approach (LCM method or efficiency method) for time-work problems.
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Key Concepts
- **Number System Basics**: Natural numbers (1, 2, 3…), Whole numbers (0, 1, 2…), Integers (…−2, −1, 0, 1, 2…), Rational numbers (p/q form), Irrational numbers (non-terminating, non-repeating decimals like √2).
- **Divisibility Rules**: A number is divisible by 3 if sum of digits is divisible by 3; by 4 if last two digits form a number divisible by 4; by 9 if digit sum divisible by 9; by 11 if difference of sums of alternate digits is 0 or divisible by 11.
- **Percentage as "Per Hundred"**: x% of Y = (x × Y)/100. Converting fractions to percentages: multiply by 100. Key equivalents: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%.
- **Ratio Expresses Relative Magnitude**: If A : B = 3 : 5, then A = 3k and B = 5k for some constant k. Ratios can be combined using LCM of common terms.
- **Profit-Loss Reference Point**: Profit or loss is always calculated on Cost Price (CP), not Selling Price (SP). Profit% = (Profit/CP) × 100.
- **Time-Work Relationship**: If A completes work in x days, A's one-day work = 1/x. Total work is often assumed as LCM of individual times for easier calculation.
- **Pipes and Cisterns Follow Same Logic**: Inlet adds, outlet subtracts; combined rate = algebraic sum of individual rates.
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Formulas / Key Facts
| Topic | Formula / Fact | |-------|----------------| | HCF-LCM Relation | HCF × LCM = Product of two numbers | | Percentage Increase | New Value = Original × (1 + r/100) | | Percentage Decrease | New Value = Original × (1 − r/100) | | Successive % Change | Net effect on 100: (a + b + ab/100)% for changes a% and b% | | Ratio Proportion | If a : b = c : d, then ad = bc (cross-multiplication) | | Profit | SP − CP (when SP > CP) | | Loss | CP − SP (when CP > SP) | | SP when Profit% given | SP = CP × (100 + P%)/100 | | SP when Loss% given | SP = CP × (100 − L%)/100 | | Time-Work (A + B together) | 1/A + 1/B = 1/T, where T = combined time | | Work-Wage Rule | Wages distributed in ratio of work done (or efficiency) |