A "30% OFF" sign on a kurta does not mean "₹30 off." It means the shop will scoop out thirty-hundredths of whatever the price happens to be — a proportional cut, not a fixed one. This picture is best felt, not read. Drag the slider below and watch the price bar shrink as you increase the discount.
The picture
Every percentage discount is a multiplication. If the marked price is P and the discount is d\%, the amount you pay is
The factor \left(1 - \tfrac{d}{100}\right) is called the multiplier. At d = 0 the multiplier is 1 and you pay the full price. At d = 100 the multiplier is 0 and the item is free. At d = 30 the multiplier is 0.70 and you pay 70\% of the marked price. The bar below is a visual of that multiplier in action for a ₹2000 marked price.
Why the bar shrinks linearly: the price you pay is 2000 \times \left(1 - \tfrac{d}{100}\right), which is a straight-line function of d. Double the discount and you double the rupee saving. The geometric object — the shaded bar — is a direct plot of that line. Each percent of discount shaves the same fixed length off the bar, because 1\% of ₹2000 is always ₹20.
Three settings worth feeling
Before reading on, drag the point to each of these three positions. Watching the bar shrink in real time makes the arithmetic feel obvious.
10\% off. The bar barely moves. You still pay ₹1800. Useful for mental checks: 10\% of a number is just that number with the decimal point shifted one place left.
50\% off. The bar is cut exactly in half. You pay ₹1000. This is the reference point every other discount is measured against — if a sign says "more than 50% off," it means the shop is keeping less money than it's giving away.
75\% off. Only a quarter of the bar remains. You pay ₹500. Notice how the last quarter of the discount (from 75 to 100) shaves off the same amount as the first quarter (from 0 to 25) — the shrinking is linear in the discount, even though it feels more dramatic visually near the end.
The fact that 25\% at the start and 25\% at the end have the same visual weight is a good guard against a common misconception: people often think "the last little bit" of a discount is a big deal, but it isn't. A jump from 70\% to 80\% off is the same ₹200 extra saving as a jump from 0\% to 10\% off.
Reading the three readouts
The readouts above the bar show three numbers that move together: the discount d, the multiplier 1 - \tfrac{d}{100}, and the rupee amount you pay. These are three names for the same thing — one expressed as a percentage off the full, one as a fraction of the full, and one as a concrete amount.
- At d = 20\%: multiplier = 0.80; pay = ₹1600.
- At d = 30\%: multiplier = 0.70; pay = ₹1400.
- At d = 45\%: multiplier = 0.55; pay = ₹1100.
In professional shop calculations — cashiers, spreadsheets, invoicing — the multiplier form is the one people use, because it collapses the "find the discount, then subtract" two-step into a single multiplication. If you later need to chain a discount with a tax, multipliers compose by multiplication, which is what makes them so neat. A 20\% discount followed by an 18\% GST is the multiplier 0.80 \times 1.18 = 0.944, or a net 5.6\% reduction, all in one line.
What the picture does not show
One subtlety the bar picture hides: the linear shrinking is exactly linear only because one base is being discounted one time. Real shopping often chains two or more percentages — a festival discount plus a store-card discount, or a discount followed by GST. In those cases you multiply multipliers, and the combined effect is no longer a simple line. Successive discounts add up to less than their sum, for the same reason that two halves of a banana give you one whole banana but three halves of half a banana give you three quarters — the base shrinks at each step.
If this is news to you, the next thing to look at is the compound percentage tower — the same idea, but with two percentages stacked.
Related: Percentages and Ratios · Fractions and Decimals · One Point, Three Names: Why 1/2, 0.5 and 50% Land in the Same Spot · Operations and Properties