Percentage — Study Notes for JKTET Paper I

Overview

Percentage is one of the most frequently tested topics in the Mathematics section of JKTET Paper I. It forms the foundation for understanding profit and loss, simple interest, discount, and data interpretation — all of which appear in the syllabus. Examiners expect candidates to convert between fractions, decimals, and percentages fluently, and to apply percentage concepts to real-world situations that primary teachers encounter.

For JKTET, you must master three core skills: converting between different forms (fraction ↔ decimal ↔ percentage), calculating percentage of a quantity, and solving word problems involving percentage increase, decrease, and comparison. Questions typically involve contexts familiar to J&K students — population data, agricultural yields, school attendance, or simple commercial transactions.

The good news: percentage problems follow predictable patterns. Once you internalise the base formula and a handful of shortcuts, you can solve most questions in under a minute. This topic rewards practice more than memorisation.

Key Concepts

• **Percentage means "per hundred"**: The symbol % represents a fraction with denominator 100. So 25% = 25/100 = 0.25.

• **The universal percentage formula**: Percentage = (Part / Whole) × 100. This single formula handles almost every percentage question.

• **Converting fraction to percentage**: Multiply the fraction by 100. Example: 3/5 = (3/5) × 100 = 60%.

• **Converting percentage to fraction**: Write percentage over 100 and simplify. Example: 45% = 45/100 = 9/20.

• **Finding percentage of a number**: X% of Y = (X/100) × Y. Example: 20% of 150 = (20/100) × 150 = 30.

• **Percentage increase**: New Value = Original + (Increase% × Original). Increase% = [(New − Original) / Original] × 100.

• **Percentage decrease**: New Value = Original − (Decrease% × Original). Decrease% = [(Original − New) / Original] × 100.

• **Base value matters**: Percentage change is always calculated on the original (base) value, not the new value.

Formulas / Key Facts

| Concept | Formula | |---------|---------| | Percentage of a quantity | X% of Y = (X × Y) / 100 | | What percentage is A of B? | (A / B) × 100 | | Percentage increase | [(New − Old) / Old] × 100 | | Percentage decrease | [(Old − New) / Old] × 100 | | Value after P% increase | Original × (1 + P/100) | | Value after P% decrease | Original × (1 − P/100) | | Successive % changes: first a%, then b% | Net effect on original = a + b + (ab/100) % |