Percentage
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What is Percentage?
A percentage is a number expressed as a fraction of 100. The word comes from Latin per centum meaning "per hundred."
Symbol: %
If you score 75 out of 100, you scored 75%.
If you score 45 out of 60, convert: (45 ÷ 60) × 100 = 75%
Why it matters for BPSC TRE 4.0:
Percentage questions appear in every paper — profit/loss, discount, population growth, and data interpretation all rely on this single concept.
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Core Formula
Percentage = (Part ÷ Whole) × 100
Finding the Part:
Part = (Percentage × Whole) ÷ 100
Finding the Whole:
Whole = (Part × 100) ÷ Percentage
Examples:
Memorize all three forms — BPSC asks all three types.
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Percentage Increase & Decrease
% Increase = [(New – Old) ÷ Old] × 100
% Decrease = [(Old – New) ÷ Old] × 100
Key rule: Always divide by the ORIGINAL (old) value, never the new one.
Example — Increase:
Price rises from ₹400 to ₹500
→ [(500 – 400) ÷ 400] × 100 = 25% increase
Example — Decrease:
Price falls from ₹500 to ₹400
→ [(500 – 400) ÷ 500] × 100 = 20% decrease
Note: 25% increase and 20% decrease bring you back to the same value — percentages differ because the base changes.
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Successive Percentage Change
When a value changes by two percentages one after another:
Net Change % = a + b + (ab ÷ 100)
Use – sign for decrease.
Example:
Price first +20%, then –10%:
Net % = 20 + (–10) + [20 × (–10) ÷ 100]
= 10 + (–2) = +8% net increase
Shortcut — equal and opposite:
+10% then –10% ≠ 0
Net = –(10²/100) = –1% (always a loss)
This is because the second % applies on a different base than the first.
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Fraction–Percentage Equivalents (Must Memorise)
These save crucial exam time — convert mentally without calculation:
Trick: To go fraction → %, multiply by 100. To go % → fraction, divide by 100 and simplify.
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Points to Remember