Arithmetic
Percentage, Ratio-Proportion, Profit-Loss and Interest
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Overview
Arithmetic forms the backbone of the quantitative section in GTET. This topic—covering percentage, ratio-proportion, profit-loss and interest—appears consistently because these concepts underpin everyday numerical reasoning that primary teachers must master and teach effectively.
For TET-1 (classes 1-5) and TET-2 (classes 6-8), expect 3-5 questions directly testing these areas. The questions are typically word problems requiring quick calculation and conceptual clarity. Mastery here also helps in data interpretation and mensuration problems where percentage calculations frequently appear.
Students must build fluency in converting between fractions, decimals and percentages, and develop the habit of identifying base values correctly. Most errors stem from confusion about "of what" a percentage is taken or mixing up cost price with selling price.
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Key Concepts
- **Percentage means "per hundred"**: 25% = 25/100 = 0.25. Always convert percentages to fractions or decimals for calculation.
- **Ratio compares two quantities of the same unit**: The ratio a:b means for every 'a' units of the first, there are 'b' units of the second. Ratios have no units.
- **Proportion states two ratios are equal**: If a:b = c:d, then ad = bc (cross-multiplication rule).
- **Cost Price (CP) is what you pay; Selling Price (SP) is what you receive**: Profit or loss is always calculated on CP unless stated otherwise.
- **Simple Interest (SI) remains constant each year**: Interest is calculated only on the original principal.
- **Compound Interest (CI) grows each period**: Interest is calculated on principal plus accumulated interest.
- **Successive percentage changes cannot simply be added**: A 10% increase followed by 10% decrease does not return to the original value.
- **"Of" in percentage problems means multiplication**: 30% of 50 = (30/100) × 50.
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Formulas / Key Facts
**Percentage**
- Percentage = (Part / Whole) × 100
- Value after x% increase = Original × (1 + x/100)
- Value after x% decrease = Original × (1 − x/100)
- Net effect of successive changes of a% and b% = (a + b + ab/100)%
**Ratio and Proportion**
- If a:b = c:d, then a×d = b×c
- To divide amount M in ratio a:b, shares are Ma/(a+b) and Mb/(a+b)