How to solve percentage problems without confusing the whole

The most useful first question is: “A percentage of which number?” Different wording can change the base, even when the percentage looks the same.

Find a discount and the final price

A bag costs 1,200 som and has a 15% discount. The discount is 1,200 × 15/100 = 180 som. The price after the discount is 1,200 − 180 = 1,020 som.

Writing both quantities prevents a common error: answering with 180 when the question asks what the customer pays.

Recover an original value

A price becomes 600 som after a 20% increase. The new price is 120% of the old price, so 1.2 × old price = 600. Divide: 600 ÷ 1.2 = 500 som.

Subtracting 20% of 600 would give 480, because it uses the new price as the base. The increase was calculated from the original 500, not from 600.

Do opposite changes cancel?

Start with 500. A 20% increase gives 600. A subsequent 20% decrease gives 600 × 0.8 = 480. The result is 4% below the original value because the second percentage uses a different base.

A check before submitting

Label the whole, the percentage amount and the requested final quantity. Estimate whether the answer should be larger or smaller. Return to the mathematics examples, then use test review to identify repeated base-selection mistakes.