Arithmetic

Percentage, Ratio-Proportion, Profit-Loss and Interest

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Overview

Arithmetic forms the backbone of quantitative aptitude in AP TET Paper I and Paper II. This topic tests your ability to handle everyday numerical problems involving percentages, ratios, profit-loss calculations, and interest computations—skills essential for teaching mathematics at the primary and upper primary levels.

Questions from this section appear consistently in the Mathematics content portion of the exam. Examiners test not just calculation speed but also conceptual clarity—whether you understand what "25% of" truly means or how simple interest differs from compound interest. Mastery here also strengthens your pedagogy responses, as you'll need to explain these concepts to young learners.

Focus on building mental math shortcuts, understanding word-problem patterns, and avoiding common traps in percentage-to-fraction conversions and ratio manipulations.

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Key Concepts

• **Percentage means "per hundred"**: x% = x/100. Converting between percentages, fractions, and decimals is foundational (e.g., 25% = 1/4 = 0.25).

• **Ratio expresses a relationship between two quantities** in the same unit. Written as a:b or a/b. Ratios have no units; they compare magnitudes.

• **Proportion states that two ratios are equal**: If a:b = c:d, then a×d = b×c (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)** is calculated on the original principal only: SI = (P × R × T)/100.

• **Compound Interest (CI)** is calculated on principal plus accumulated interest. Amount A = P(1 + R/100)^T.

• **Successive percentages** don't simply add. A 10% increase followed by a 10% decrease does not return to the original—it results in a 1% net decrease.

• **Ratio of division** problems require understanding that if a sum S is divided in ratio a:b, the parts are S×a/(a+b) and S×b/(a+b).

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Formulas / Key Facts

| Concept | Formula / Fact | |---------|----------------| | Percentage to Fraction | x% = x/100 | | Finding x% of a number N | (x/100) × N | | Percentage Increase | [(New − Old)/Old] × 100 | | Percentage Decrease | [(Old − New)/Old] × 100 | | Ratio a:b as fraction | a/(a+b) and b/(a+b) of the whole | | Proportion (cross-multiply) | If a:b = c:d, then ad = bc | | Profit | SP − CP (when SP > CP) | | Loss | CP − SP (when CP > SP) | | Profit % | (Profit/CP) × 100 | | Loss % | (Loss/CP) × 100 | | SP when Profit % given | SP = CP × (100 + Profit%)/100 | | SP when Loss % given | SP = CP × (100 − Loss%)/100 | | Simple Interest | SI = (P × R × T)/100 | | Amount (SI) | A = P + SI = P(1 + RT/100) | | Compound Interest Amount | A = P(1 + R/100)^T | | CI | CI = A − P |