Study Notes: Percentage

Overview

Percentage is one of the most frequently tested topics in SSC MTS Paper 1, appearing in 3–5 questions every year. The word "percent" means "per hundred," so 25% literally means 25 out of 100 or 25/100. Mastering percentage is critical because it forms the foundation for profit and loss, simple interest, data interpretation, and discount problems.

In SSC MTS, percentage questions test three core skills: converting between fractions/decimals/percentages, calculating percentage increases or decreases, and solving word problems involving successive changes, population changes, exam pass percentages, or salary adjustments. The questions are straightforward but require speed and accuracy. Students who master the basic formulas and practice mental calculation techniques can solve most percentage problems in under 60 seconds.

The key to success is understanding that percentage is just another way to express ratios and fractions, combined with the ability to quickly apply the standard formulas for percentage change and successive percentage changes without confusion.

Key Concepts

• **Percentage as a fraction**: x% means x/100. To convert any fraction to percentage, multiply by 100. To convert percentage to fraction, divide by 100 and simplify.

• **Percentage of a quantity**: To find x% of N, calculate (x/100) × N. This is the base formula for all percentage calculations.

• **Percentage change formula**: Percentage change = [(New Value − Original Value) / Original Value] × 100. Positive result means increase, negative means decrease.

• **Reverse percentage problem**: If x% of a number is given and you need the number itself, use: Number = (Given Value × 100) / x.

• **Successive percentage changes**: When two percentage changes happen one after another, they don't simply add. Use the formula: Net change = a + b + (ab/100), where a and b are the two percentage changes (use negative sign for decrease).

• **Comparing quantities using percentage**: "A is what percent more/less than B?" = [(A − B) / B] × 100. Always divide by the reference value (the one mentioned after "than").

Formulas / Key Facts

1. **Basic conversion**: x% = x/100 = 0.0x in decimal form 2. **Percentage of N**: x% of N = (x/100) × N = xN/100 3. **Increase by x%**: New Value = Original × (1 + x/100) = Original × (100 + x)/100 4. **Decrease by x%**: New Value = Original × (1 − x/100) = Original × (100 − x)/100 5. **Percentage increase**: [(Increase) / Original] × 100 6. **Percentage decrease**: [(Decrease) / Original] × 100 7. **Successive changes**: If increased by a% then by b%, net = a + b + (ab/100)% 8. **Common fraction-percentage conversions**: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/3 = 33.33%, 2/3 = 66.67%, 1/8 = 12.5%, 3/4 = 75%