Math · Aptitude · Chapter 01

💯 Percentage

Per-hundred math — convert, calculate, compare.

💡 What is Percentage?

Percent (%) means "out of 100". So 35% means 35 out of every 100, or 35/100 = 0.35.

Three core conversions you should be able to do instantly:

% → Fraction
25% = 25/100 = 1/4
% → Decimal
35% = 0.35
Fraction → %
3/4 = 3/4 × 100 = 75%
x% of y
x% of y = (x × y) / 100

Percentage change (increase or decrease):

% change = (New − Old) / Old × 100

Example: Salary went from ₹20,000 to ₹25,000 → change = (25000−20000)/20000 × 100 = 25% increase.

⚡ Fraction-to-% table (memorize this!)

1/2 = 50% · 1/3 = 33.33% · 1/4 = 25% · 1/5 = 20% · 1/6 = 16.67% · 1/7 ≈ 14.28% · 1/8 = 12.5% · 1/9 ≈ 11.11% · 1/10 = 10% · 1/11 ≈ 9.09% · 1/12 ≈ 8.33% · 1/16 = 6.25% · 1/20 = 5% · 1/25 = 4%

Why memorize? If you see "increased by 16.67%" you immediately know it means "× 7/6" — much faster than calculating.

⚡ Successive percentage trick

If a number is increased by a% then by b%, net change = a + b + (ab/100).
Example: Price ↑20% then ↑10% → net = 20 + 10 + (200/100) = 32% increase (not 30%!).

For decrease, use negative values. ↑20% then ↓20% → 20 + (−20) + (20×−20/100) = −4% (net loss!).

🎬

The 100-Square — Visual Percentage

Animation
EACH CELL = 1% — FILLED CELLS SHOW THE PERCENTAGE CONVERSIONS 35% AS FRACTION 7/20 AS DECIMAL 0.35 35% of 200 = 70

100-cell grid where each cell is 1%. Drag the slider below to see different percentages.

🧮

Percentage Calculator

Calculator

Slide to see the 100-grid. Then try the real calculators below.

35%
📐 Find x% of y

% of = 200

📈 % change calculator

From ₹ to ₹ = +25%

🔀 Successive % (compound effect)

First % then % = net +32%

Formula: a + b + ab/100. Here: 20 + 10 + (20×10)/100 = 32%.

Practice: If a number is first increased by 20% and then decreased by 20%, what is the net % change?
Answer: −4% (net decrease). Apply formula: 20 + (−20) + (20 × −20)/100 = 0 − 4 = −4%. Many students assume "no change" — that's wrong because percentages compound multiplicatively, not additively.