Discounts and Taxes

A cooker has a displayed price of ₹1800, and the shop offers 35% off. Nearby, a bill adds a percentage tax to another item. Both use percentages, but one reduces a quoted price and the other increases the amount payable. To calculate correctly, you must identify what amount the percentage applies to and whether you are finding the reduction, the extra charge or the final payment. The words around the numbers are as important as the numbers themselves.

A discount also does not automatically imply a loss for the seller. The marked price might be far above the buying cost. After reducing it, the seller could still receive more than the cost price and make a profit.

We will follow the money through these stages and then consider the difference between the gross profit from goods and the amount left after other business expenses.

A 35% discount means that 35 out of every 100 equal parts of the marked price are removed. The customer pays the remaining 65%. For the ₹1800 cooker, the discount is 0.35 × 1800 = ₹630, and the selling price before any separately added tax is ₹1170.

The discount percentage uses marked price as its base. This differs from profit percentage on cost, which uses cost price. Writing MP, SP and CP beside the amounts helps you keep these calculations separate.

There are two reliable methods. Find the discount amount and subtract it, or multiply the marked price directly by the remaining percentage. The second method is shorter, but the first can be useful when a bill shows the discount separately.

To recover a marked price, reverse the discount multiplier. If a discounted price is ₹680 after 15% off, the ₹680 represents 85% of the marked price. Dividing by 0.85 gives ₹800.

Adding 15% to ₹680 would give ₹782, which does not undo the original discount. That new 15% is based on a smaller amount. Undoing a percentage change requires division by its multiplier.

Taxes

A percentage tax is calculated on a stated taxable amount. If an item costs ₹8250 before tax and the problem specifies a tax of 18%, the tax amount is 18% of ₹8250. Adding that amount produces the final payment.

Use the rate supplied in a mathematical problem; the examples here are calculations with stated rates, not claims about the current rate on a product. Real bills may specify whether a price already includes tax. Applying tax again to an inclusive price would count it twice.

When a bill contains a discount followed by a tax, identify the taxable amount explicitly. In the following model, tax is charged on the price after discount. The order of the displayed calculations should make that base visible.

The tax collected for the government is not automatically the seller’s profit. In the last example, the customer pays ₹1890, but ₹90 has been identified as tax. The seller’s sale amount before that tax is ₹1800. A profit calculation must treat these roles consistently.

For a bill-checking activity, read the labels before checking arithmetic. Determine whether the tax base is the original price, the discounted price or another explicitly stated amount. Mathematics can verify a stated calculation without assuming how every real bill must be arranged.

Profit from buying and selling goods is called gross profit when it is calculated as sales revenue minus the cost of those goods. A business may also pay rent, wages, electricity or transport charges that are listed separately. Subtracting those additional expenses from gross profit gives net profit in this simplified account.

Suppose monthly sales are ₹80,000 and the goods sold cost ₹48,000. Gross profit is ₹32,000. If separately listed expenses are ₹8000, net profit is ₹24,000. Net profit answers how much remains after those expenses, so it is less than gross profit.

A percentage must still name its base. The ₹24,000 net profit is 30% of ₹80,000 revenue. Comparing it with another amount would answer a different question. The phrase “profit percentage” without a base can be ambiguous in business contexts; state “on cost” or “of revenue” explicitly.