Profit, loss and discount

Shopping has three prices, and it pays to keep them apart:

The labels depend on who's speaking. A sweater's selling price at the wholesaler is the retailer's cost price. Follow one sweater from the maker to the customer and each step relabels the same rupees.

Kishanlal buys a sweater at ₹300, marks it ₹480, and after bargaining sells it for ₹430. The selling price is above the cost price, so he makes a profit of ₹430 − ₹300 = ₹130. Had he sold below ₹300, it would have been a loss.

Percentage profit is measured against the cost price, what he put in: (130/300) × 100 = 43.3%.

A loss works the same way. Raghu bought 10 kg of rice at ₹35 a kg (₹350) and cleared it for ₹300. The loss is ₹50, and the percentage loss is (50/350) × 100 = 14.28%.

Now backwards. Shyamala's vase cost ₹2650 and she'll sell at an 18% loss. Either take 18% off: 18% of 2650 = 477, so 2650 − 477 = ₹2173. Or see that the selling price is 82% of the cost: 0.82 × 2650 = ₹2173. The second is one step shorter, and both are right.

A discount is the same idea from the customer's side: '30% off' means the shop will reduce the price by 30%. A discount is measured against the marked price.

Two words about profit that often get mixed up. Kishanlal sells ₹80,000 of goods that cost him ₹48,000: a gross profit of ₹32,000. Take away his other expenses (transport, salaries, electricity) of ₹8,000, and what's left, ₹24,000, is net profit.

And the base matters. Manisha buys fertiliser at ₹500 a bag and sells at ₹750. Against what she invested, that's (250/500) × 100 = 50%; against what she earned, it's (250/750) × 100 = 33.33%. Both are true; they answer different questions.

Finally, GST and income tax are percentages too: part of what you pay goes to the government (on a bill, CGST to the central government and SGST to the state). Look at the next bill you see and check its arithmetic.