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Class 8 — Comparing Quantities

Discounts: the money comes out of your profit

Every child's first instinct when sales are slow is to cut the price. It usually works — more people buy. And it very often makes the day worse, because a 20% discount is not 20% off the price, it is closer to half your profit.

The calculation is the easy part

Discount = marked price × rate ÷ 100. Selling price = marked price − discount. A Class 8 student can do this in a line.

The hard part is what the answer means, and no textbook question ever asks.

Where the money actually comes from

Your cost does not fall when you discount. So the whole discount comes out of the gap between cost and price — which is your profit.

A glass costing ₹7 sold at ₹12 makes ₹5. Discount it 20% and you sell at ₹9.60, making ₹2.60. The price fell by a fifth. The profit fell by almost half.

That asymmetry is the single most useful thing a Class 8 student can take out of this chapter, and it is the reason a busy discount day can still end in a loss.

A worked example from a real day

Marked price₹12
Cost to make one glass₹7
Profit before discount₹5
Discount offered20% = ₹2.40
Profit after discount
price −20%, profit −48%
₹2.60
Extra glasses needed to break even on the choiceabout 9 in every 10 more

The discount is only worth it if it brings enough extra customers to cover the profit it destroys. That is a calculation, not a hunch — and it is one most adults never do.

Try it: what is that discount really costing you?

A discount comes out of your profit, not out of your price.
₹2.40
off the price — your profit falls from ₹5 to ₹2.60

Practice

A ₹250 item is offered at 15% off. What is the selling price?
Show the answer
₹212.50
250 × 15 ÷ 100 = ₹37.50 discount. 250 − 37.50 = ₹212.50.
An item costs ₹40 to make and is marked at ₹60. After a 25% discount, what is the profit?
Show the answer
₹5
Discount = 60 × 25 ÷ 100 = ₹15. Selling price = ₹45. Profit = 45 − 40 = ₹5. The profit fell from ₹20 to ₹5 — a 75% fall from a 25% discount.
A shop marks at ₹80 and gives 10% off, still making ₹22 profit. What did the item cost?
Show the answer
₹50
Selling price = 80 − 8 = ₹72. Cost = 72 − 22 = ₹50.

Learn it by running one

In Lemonade Empire your child runs a lemonade cart and uses this exact concept to decide what to buy and what to charge. Free, no signup, plays in a browser.

▶ Play Lemonade Empire free

Common questions

How do you calculate discount percentage?
Discount ÷ marked price × 100. To find the selling price, subtract the discount from the marked price.
Why do shops give discounts if it costs them profit?
Because they expect the extra volume to more than cover it, or they need to clear stock that will otherwise spoil. Both are worth working out rather than guessing — perishable stock is a good reason, a slow afternoon usually is not.

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