Percentage and Ratio

Overview

Percentage and Ratio form the quantitative backbone of the TN TET Mathematics section. These concepts appear directly in exam questions and also underpin topics like profit-loss, simple interest, data interpretation and time-work problems. A strong grasp here means faster problem-solving across multiple question types.

For TN TET, expect questions that test your ability to convert between fractions, decimals and percentages, find percentage increase/decrease, simplify ratios, apply proportion rules and solve word problems using the unitary method. These are not just calculation questions—they require conceptual clarity about what "per hundred" means and how quantities relate to each other. Mastering this topic builds the foundation for teaching these concepts effectively to primary and upper-primary students.

Key Concepts

• **Percentage means "per hundred"**: 25% literally means 25 out of 100, written as 25/100 or 0.25. Always think of percentage as a fraction with denominator 100.

• **Ratio compares two quantities of the same kind**: A ratio 3:5 means for every 3 units of the first quantity, there are 5 units of the second. 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 rule). This is the foundation for solving proportion problems.

• **Unitary method finds the value of one unit first**: If 5 pens cost ₹40, one pen costs ₹40÷5 = ₹8. From this unit value, you can find the cost of any number of pens.

• **Percentage change = (Change ÷ Original) × 100**: Whether increase or decrease, always divide by the original (starting) value, not the new value.

• **Successive percentages don't add directly**: A 10% increase followed by 10% decrease does NOT bring you back to the original. The net effect must be calculated step by step.

• **Part-to-whole vs part-to-part**: Ratios can express parts to whole (like 2 out of 5) or parts to parts (like 2:3). Converting between these is essential.

Formulas / Key Facts

| Concept | Formula/Fact | |---------|--------------| | Percentage to fraction | x% = x/100 | | Fraction to percentage | (a/b) × 100% | | Percentage of a number | x% of N = (x/100) × N | | Percentage increase | [(New − Original) ÷ Original] × 100 | | Percentage decrease | [(Original − New) ÷ Original] × 100 | | If A is x% more than B | A = B × (1 + x/100) | | If A is x% less than B | A = B × (1 − x/100) | | Ratio a:b in fraction form | a/(a+b) and b/(a+b) of total | | Proportion rule | If a:b = c:d, then ad = bc | | Successive % change | Final = Original × (1 ± p/100) × (1 ± q/100) | | Common fraction-percent pairs | 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, 1/3 ≈ 33.33% |