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Class 7–8 — Comparing Quantities

Percentages: how much of every rupee do you keep?

Two shopkeepers both made ₹200 today. One is doing well and the other is in trouble, and the only way to tell them apart is a percentage. This is where Comparing Quantities stops being a chapter and starts being a decision.

A percentage is a comparison, not a quantity

₹200 profit on ₹400 of sales is 50%. ₹200 profit on ₹4,000 of sales is 5%. Same profit, completely different business.

Margin is the percentage of every rupee of sales that you keep. It is what lets you compare a good day against a big day.

How to work it out

Profit ÷ selling price × 100. That is it.

The part worth arguing about is what belongs in the cost. Miss the rent and your margin looks better than it is — which is exactly how a business runs out of money while its owner believes it is profitable.

A worked example from a real day

Sales for the day₹456
Everything spent₹232
Profit₹224
Margin
of every ₹1 taken, 49 paise stayed
224 ÷ 456 × 100 = 49%
A 20% margin day for comparison₹91 profit on the same ₹456

Same cart, same street, same number of customers. The difference between a 49% day and a 20% day is entirely in what was paid for stock and what was charged — two decisions, made before a single glass was sold.

Try it: how much are you actually keeping?

Cost is what you spend. Price is what you charge. Margin is what survives.
41%
₹5 profit on every ₹12 of sales

Practice

A stall takes ₹600 and keeps ₹150. What is the margin?
Show the answer
25%
150 ÷ 600 × 100 = 25.
What is 15% of ₹240?
Show the answer
₹36
240 × 15 ÷ 100 = 36.
A glass costs ₹8 to make. What price gives a 20% margin?
Show the answer
₹10
At a 20% margin, cost is 80% of the price. 8 ÷ 0.8 = ₹10. Note it is not ₹8 + 20%.

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

What is a good profit margin for a small business?
It varies enormously by trade, so the useful skill is not memorising a number but being able to calculate your own and compare it week to week.
Why is margin better than profit for judging a day?
Profit tells you how much. Margin tells you how efficiently. A big day with a thin margin is fragile — one bad break and it becomes a loss.
My child can do percentage sums but not word problems. Why?
Almost always because they cannot tell which number is the whole. In a business the whole is obvious — it is what came in — which is why applied practice fixes this faster than more sums.

Next concepts

Profit & lossClass 7 — Comparing Quantities DiscountsClass 8 — Comparing Quantities Break-evenClass 8 — Linear Equations