Introduction to Percentage

What is Percentage?

Percent means "per hundred". A percentage expresses a number as a fraction of 100, so 25% = 25/100 = 1/4. Percentage questions appear in almost every RRB NTPC Mathematics section.

Key formulas

• x% of y = (x/100) × y
• Fraction to percentage: multiply by 100 (3/5 × 100 = 60%)
• Percentage to fraction: divide by 100 (40% = 2/5)
• Percentage change = (Change ÷ Original value) × 100
• Successive change of a% and b%: net = a + b + (a × b)/100 (use a negative sign for a decrease)

Useful equivalents

• 1/2 = 50%, 1/4 = 25%, 3/4 = 75%
• 1/5 = 20%, 1/8 = 12.5%, 1/10 = 10%
• 1/3 = 33.33%, 1/6 = 16.67%

Quick example

Q. A ticket price rises from ₹200 to ₹250. Find the percentage increase.

A. Increase = 50. Percentage increase = (50 ÷ 200) × 100 = 25%.

Common trap

A 10% increase followed by a 10% decrease does not bring you back to the start: net = 10 − 10 − (10 × 10)/100 = −1%, i.e. a 1% decrease.

Analogy

Analogy: A cricket score out of 100 balls

Imagine every quantity is converted into an innings of exactly 100 balls.

• If a batter scores 25 runs in every 100 balls, that is 25% — a percentage simply means "how many out of 100".
• Comparing two batters who faced different numbers of balls is hard; converting both to "per 100 balls" makes it fair. Percentages do the same for marks, prices and population.
• When the base changes (a new innings), the same runs give a different percentage — which is why a 10% rise followed by a 10% fall does not return you to the start.

Always ask: "Out of 100 of what?" — the base decides the answer.