Percentage Made Easy: Marks, Discounts, Increase, Decrease and Reverse Percentage

“Percent” just means “per hundred”: 18% is 18 out of every 100. That is the whole definition, and yet marks, discounts, salary hikes and GST bills trip people up every day, mostly because they are four different questions that all use the same word. This guide separates the four, gives each a formula and a mental shortcut, and shows the two traps that catch even careful people. Every figure is produced by the same functions that power our percentage calculator; the GST and discount rates used are examples, not a statement of any current rate.

The four questions

Decide which shape you have before touching a calculator. Most mistakes come from using the formula for one shape on another.

1. Marks: X is what percent of Y

Formula: percentage = part ÷ whole × 100.

432 out of 500 is 432 ÷ 500 × 100 = 86.4%. 96 out of 120 is 80%.

Shortcut: when the maximum is a factor or multiple of 100 the division is trivial: out of 500, double the marks and divide by 10 (432 → 864 → 86.4); out of 50, double (43 → 86%); out of 25, multiply by 4; out of 200, halve. For an aggregate across subjects, add all the marks and all the maximums first, then divide once; do not average the subject percentages unless every subject has the same maximum.

2. Part of a whole: X percent of Y

Formula: part = percent ÷ 100 × whole.

18% of ₹2,500 is 0.18 × 2,500 = ₹450, which is what an 18% tax on a ₹2,500 bill adds. 12.5% of 1,800 is 225.0.

Shortcuts:

• Start from 10%. 10% is the number with the decimal point moved one place left. 10% of 2,500 is 250; 5% is half of that (125); 1% is a tenth (25). So 18% = 10% + 5% + 1% + 1% + 1% = 250 + 125 + 75 = 450. Any percentage is a sum of these.
• Swap the numbers. X% of Y equals Y% of X. 8% of 50 looks awkward; 50% of 8 is obviously 4. 16% of 25 = 25% of 16 = 4.
• Use fractions. 25% is a quarter, 12.5% an eighth, 33.3% a third, 20% a fifth, 75% three quarters.

3. Discounts and hikes: increase or decrease by a percentage

Formula: new value = old × (1 ± percent ÷ 100).

A ₹1,499 item at 30% off costs 1,499 × 0.70 = ₹1,049.30. A ₹42,000 salary with an 8% hike becomes 42,000 × 1.08 = ₹45,360.

Shortcut: multiply by what remains, not by what is removed. 30% off means you pay 70%: 1,499 × 0.7. For a hike, multiply by 1 plus the rate: × 1.08. One multiplication instead of a subtraction after a multiplication.

The percentage change itself, when you know both values:

Formula: change % = (new − old) ÷ old × 100. The denominator is always the old (starting) value.

Rent going from ₹50,000 to ₹56,000 is +12%; a score falling from 80 to 60 is -25%. Notice the last two rows: 100 → 120 is +20% but 120 → 100 is −16.67%, not −20%, because the base changed. A 20% rise followed by a 20% fall does not return to the start: 100 → 120 → 96.

4. Reverse percentage: what was it before?

This is the shape people get wrong most. “A bill of ₹1,180 includes 18% tax; what was the price before tax?” The tempting answer, 18% of 1,180 subtracted, is wrong, because the 18% was applied to the original price, not to the final one.

Formula: original = final ÷ (1 ± percent ÷ 100).

• Price before an 18% addition, final ₹1,180: 1,180 ÷ 1.18 = ₹1,000. Check: 18% of 1,000 is 180, and 1,000 + 180 = 1,180.
• Price before a 30% discount, final ₹840: 840 ÷ 0.70 = ₹1,200. Check: 30% off 1,200 is 360, leaving 840.

The calculator’s “original value” mode does this division for you; enter the percentage as negative for a discount.

Two traps

Successive percentages do not add

A shop offers “20% off, plus an extra 10% off at checkout”. That is not 30% off. The 10% is taken from the already-reduced price: ₹1,000 → ₹800 → ₹720, which is a total discount of 28%, the same as a single 28% discount (₹720), not 30% (₹700). The same applies to two successive hikes, two years of inflation, and the compounding in our compound interest guide: multiply the factors (0.8 × 0.9 = 0.72), never add the percentages.

Percent versus percentage points

If a rate rises from 4% to 6%, it has risen by 2 percentage points but by 50% (6 is half as much again as 4). News reports and loan letters mix the two; when a bank says the interest rate “increased by 0.5%”, it almost always means 0.5 percentage points. When you compare two percentages, say “points” for the difference and reserve “percent” for the relative change.

Quick reference

X is what % of Y:        X ÷ Y × 100
X % of Y:                X ÷ 100 × Y
Increase Y by X %:       Y × (1 + X ÷ 100)
Decrease Y by X %:       Y × (1 − X ÷ 100)
% change old → new:      (new − old) ÷ old × 100
Original before X %:     final ÷ (1 ± X ÷ 100)
Two changes a % and b %: factor = (1 ± a/100) × (1 ± b/100)

All six live in the percentage calculator, which rounds to two decimals the way marksheets and bills do.

Frequently asked questions

How do I calculate the percentage of marks? Marks obtained ÷ maximum marks × 100. For a total across subjects, add all marks and all maximums first: 432 ÷ 500 × 100 = 86.4%.

How do I find a price before GST or before a discount? Divide, do not subtract: final ÷ 1.18 for an 18% addition, final ÷ 0.70 for a 30% discount. The rate is an example; use the rate on your bill.

Is 20% off then 10% off the same as 30% off? No. It is 28% off, because the second discount applies to the reduced price.

What is the difference between percent and percentage points? Points measure the gap between two percentages (4% to 6% is 2 points); percent measures the relative change (that gap is a 50% rise).

Why is a 20% fall not undone by a 20% rise? Because the base changes: 100 falls to 80, and 20% of 80 is only 16, giving 96. You need a 25% rise to get back to 100.