Arithmetic
Percentage, Ratio-Proportion, Profit-Loss and Interest
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Overview
Arithmetic forms the backbone of quantitative reasoning in KTET Mathematics. This topic covers four interconnected concepts—percentage, ratio-proportion, profit-loss, and interest—that appear both as direct calculation questions and as word problems requiring multi-step reasoning.
For KTET Categories I and II, expect 3-5 questions testing these concepts, often framed as real-life scenarios involving shopping, banking, or classroom situations. Mastery here also strengthens your ability to teach these topics effectively to primary and upper-primary students, which aligns with KTET's dual focus on content knowledge and pedagogical competence.
Students must build fluency in quick conversions (fractions to percentages, ratios to fractions) and develop mental math shortcuts. These skills transfer directly to data interpretation and mensuration problems as well.
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Key Concepts
- **Percentage means "per hundred"**: 25% = 25/100 = 0.25 = 1/4. Always convert to the most convenient form for calculation.
- **Ratio compares two quantities of the same kind**: Written as a:b or a/b. Ratios have no units—they are pure numbers.
- **Proportion states that two ratios are equal**: If a:b = c:d, then a×d = b×c (cross-multiplication property).
- **Cost Price (CP) and Selling Price (SP) determine profit or loss**: Profit = SP − CP when SP > CP; Loss = CP − SP when CP > SP.
- **Profit% and Loss% are always calculated on CP**: This is a standard convention that students often forget.
- **Simple Interest (SI) remains constant each year**: Interest is calculated only on the principal amount.
- **Compound Interest (CI) grows because interest earns interest**: Each year's interest is added to principal before calculating next year's interest.
- **Marked Price and Discount**: Discount is calculated on Marked Price (MP), not on CP. SP = MP − Discount.
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Formulas / Key Facts
**Percentage**
- Percentage = (Value / Total) × 100
- To find x% of y: (x/100) × y
- Percentage increase = [(New − Original) / Original] × 100
- Percentage decrease = [(Original − New) / Original] × 100
**Ratio and Proportion**
- If a:b = c:d, then ad = bc (product of extremes = product of means)