Successive discounts: calculate the real reduction

A new percentage base at each step

A price of 200 is reduced by 30%, then by 15% of the reduced price. The first reduction removes 60 and leaves 140. The second removes 21, leaving 119. You saved 81, or 40.5% of the original price. Adding 30 and 15 would give 45%, but that incorrectly treats both reductions as percentages of the same original base.

Use the remaining fractions

After a 30% discount, 70% remains. After the next 15%, you keep 85% of that remaining amount. Multiply 0.70 by 0.85: the product is 0.595. The final price therefore represents 59.5% of the original, and the combined reduction is 40.5%. This is the arithmetic for the stated offer, not a claim that every retailer combines promotions on the same terms.

Work backward from the final price

Suppose the final price is 119 and you know those two percentage reductions were applied without other charges or rounding changes. Divide by the remaining fraction: 119 divided by 0.595 gives 200. A 40.5% increase on 119 would not undo the reduction, because that increase uses 119 as its base. The inverse operation is division by the remaining fraction, not adding back the discount percentage.

Check rounding separately

Consider 19.99 with the same reductions. Multiplying without intermediate rounding gives 11.89405. If the seller rounds the first reduced price to 13.99, the second step gives 11.8915 before final rounding. Both may become 11.89 under ordinary rounding to two decimals, but identical final amounts in this example do not prove that intermediate rounding never matters. Follow the offer’s stated method rather than assuming one universal checkout rule.

Read the rule before applying the formula

A fixed voucher, excluded item, delivery charge or minimum basket amount changes the calculation. Establish whether the second percentage applies to the reduced price and whether the offer concerns the same item. For a quick self-check on the pure-percentage example, reverse the order: a 15% discount on a price of 200 leaves 170. Applying a 30% discount to 170 leaves 119. This check applies to multiplication without extra conditions.

Explain the method before adding speed

Practise by naming the base aloud at every step, and check an inverse calculation before trying another price. Numvolt’s untimed Zen mode and explanations after mistakes support practising calculation methods; timed rounds are a separate choice. These shopping examples are an independent worksheet, not a promise that the app includes a retail-discount module. The percentage guide explains the basics; this example concentrates on successive reductions, inversion and rounding. This guide is published by the app’s developer.

Further reading

• Roméo Apps, percentages guide (publisher source)