Arithmetic

Percentage, Ratio-Proportion, Profit-Loss and Interest

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Overview

Arithmetic forms the backbone of the Mathematics section in TS TET Paper I and Paper II. This topic tests your ability to apply fundamental operations to real-world problems involving money, comparisons, and growth over time. Questions typically appear as word problems requiring quick mental math and formula application.

For TS TET, you must master the interconversion between percentages, fractions, and decimals, understand how ratios scale quantities, calculate profit/loss in trade scenarios, and compute simple and compound interest. These concepts also form the foundation for teaching primary and upper primary students, so expect pedagogy-linked questions on how to explain these ideas using real-life examples.

Speed and accuracy matter. Memorise key fraction-percentage equivalents, practise mental shortcuts, and always verify units in word problems.

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Key Concepts

• **Percentage** means "per hundred." It standardises comparisons by expressing a part as a fraction of 100. Converting between fraction, decimal, and percentage is essential.

• **Ratio** compares two quantities of the same kind (a:b), while **proportion** states that two ratios are equal (a:b = c:d). Cross-multiplication solves most proportion problems.

• **Profit and Loss** measure gain or loss relative to the Cost Price (CP). Profit = SP − CP; Loss = CP − SP. Percentages are always calculated on CP unless stated otherwise.

• **Simple Interest (SI)** grows linearly—interest is calculated only on the principal. **Compound Interest (CI)** grows exponentially—interest is added to principal each period.

• **Marked Price (MP)** and **Discount** are common in retail problems. Discount is calculated on MP, not CP.

• In ratio problems, the **constant of proportionality** (k) helps find actual quantities when only the ratio and sum/difference are given.

• **Successive percentages** (like two discounts or two increases) cannot simply be added; use the net effect formula.

• **Population and depreciation** problems use compound interest logic with growth rate (+r) or decay rate (−r).

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Formulas / Key Facts

| Concept | Formula | |---------|---------| | Percentage of a number | (Percentage × Number) / 100 | | Fraction to Percentage | (Fraction) × 100% | | Percentage Change | [(New − Old) / Old] × 100% | | Ratio a:b in fractions | a/(a+b) and b/(a+b) of total | | Proportion (cross-multiply) | If a:b = c:d, then a×d = b×c | | Profit | SP − CP | | Loss | CP − SP | | Profit % | (Profit / CP) × 100 | | Loss % | (Loss / CP) × 100 | | SP when Profit % given | CP × (100 + Profit%) / 100 | | SP when Loss % given | CP × (100 − Loss%) / 100 | | Discount | MP − SP | | Discount % | (Discount / MP) × 100 | | Simple Interest | SI = (P × R × T) / 100 | | Amount (SI) | A = P + SI = P(1 + RT/100) | | Compound Interest | A = P(1 + R/100)^T | | CI | A − P | | Successive % change | Net = a + b + (ab/100) for two changes a% and b% |