Percentage — Study Notes for JTET Paper I

Overview

Percentage is one of the most practical and frequently tested topics in JTET Paper I Mathematics. The word "percent" comes from the Latin "per centum," meaning "per hundred." A percentage is simply a way of expressing a number as a fraction of 100, making it easier to compare quantities of different sizes.

This topic forms the foundation for many real-life calculations—discounts in shops, marks obtained in exams, population growth, and bank interest rates. For JTET, you must be comfortable converting between fractions, decimals, and percentages, and solving word problems involving increase, decrease, and comparison. Questions typically test both computational speed and conceptual clarity, so mastering the underlying logic is essential.

Percentage also connects directly to other Paper I topics like Profit-Loss-Discount and Simple Interest. A strong grip here will make those topics significantly easier.

Key Concepts

• **Percentage means "out of 100"**: 25% means 25 out of every 100, written as 25/100 or 0.25 in decimal form.

• **Conversion trio**: Any percentage can be written as a fraction (divide by 100) or decimal (move decimal point two places left), and vice versa. Example: 40% = 40/100 = 2/5 = 0.40.

• **Finding percentage of a quantity**: To find x% of a number N, calculate (x/100) × N. Example: 15% of 200 = (15/100) × 200 = 30.

• **What percentage is A of B?**: Use the formula (A/B) × 100. Example: 45 is what percent of 180? Answer: (45/180) × 100 = 25%.

• **Percentage increase**: When a value rises from old to new, increase% = [(New − Old)/Old] × 100.

• **Percentage decrease**: When a value falls, decrease% = [(Old − New)/Old] × 100.

• **Successive percentage change**: If two successive changes of a% and b% occur, net effect = a + b + (ab/100). This can be positive or negative depending on increase/decrease.

• **Reverse percentage (finding original)**: If a number after x% increase becomes N, the original = N × (100/(100 + x)).

Formulas / Key Facts

| Formula / Fact | Context | |----------------|---------| | x% of N = (x × N)/100 | Finding a percentage of any quantity | | (A/B) × 100 = percentage | Finding what percent A is of B | | Increase% = [(New − Old)/Old] × 100 | Calculating percentage increase | | Decrease% = [(Old − New)/Old] × 100 | Calculating percentage decrease | | Net change = a + b + (ab/100) | Successive changes of a% and b% | | Original = Final × [100/(100 ± change%)] | Finding original after increase (+) or decrease (−) | | 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5% | Common fraction-percentage equivalents | | 1/3 = 33.33%, 2/3 = 66.67%, 1/6 = 16.67% | Recurring decimal percentages | | If A is x% more than B, then B is [x/(100+x)] × 100% less than A | Reverse comparison between two quantities |