Ratio, Proportion, Percentages, Profit-Loss

Overview

This topic forms the backbone of commercial mathematics at the primary level and appears consistently in MAHA TET Paper I and Paper II. Questions test your ability to apply these concepts to everyday situations—sharing sweets among children, calculating discounts at shops, or finding profit earned by a vendor. The examiner values conceptual clarity over rote memorisation.

For TET aspirants, mastery here serves two purposes: answering content questions correctly and understanding how to teach these interconnected concepts to young learners. Expect 3–5 questions combining ratio-proportion with percentage or profit-loss applications. Speed and accuracy come from understanding the underlying relationships rather than memorising isolated formulas.

The concepts build upon each other—ratio leads to proportion, proportion connects to percentages, and percentages underpin profit-loss calculations. Teach them in this sequence for both exam success and classroom effectiveness.

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Key Concepts

• **Ratio** compares two quantities of the same kind using division. The ratio of a to b is written as a : b or a/b. Order matters: 3 : 5 is different from 5 : 3.

• **Equivalent ratios** are obtained by multiplying or dividing both terms by the same non-zero number. Example: 2 : 3 = 4 : 6 = 6 : 9.

• **Proportion** states that two ratios are equal. If a : b = c : d, then a, b, c, d are in proportion. The product of extremes equals the product of means: a × d = b × c.

• **Percentage** means "per hundred." To convert a fraction to percentage, multiply by 100. To convert percentage to fraction, divide by 100.

• **Cost Price (CP)** is what a seller pays to acquire goods. **Selling Price (SP)** is what the buyer pays to the seller.

• **Profit** occurs when SP > CP. **Loss** occurs when SP < CP. Both are always calculated on Cost Price.

• **Discount** is the reduction from Marked Price (MP). Selling Price = Marked Price − Discount.

• **Unitary method** finds the value of one unit first, then scales to the required quantity—essential for proportion problems.

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Formulas / Key Facts

| Concept | Formula | |---------|---------| | Ratio simplification | Divide both terms by their HCF | | Proportion test | a : b :: c : d ⟹ a × d = b × c | | Fraction to percentage | (Fraction) × 100% | | Percentage to fraction | (Percentage) ÷ 100 | | Finding X% of Y | (X/100) × Y | | 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 | | Discount | MP − SP | | Discount % | (Discount/MP) × 100 |