Ratio, proportion and percentages

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# 3.4 Decreasing by a percentage

Discount can be calculated in the same way as an increase by a percentage. For example, £8 with 15% discount means you actually pay

£8 less (15% of £8)

15% of 8 = × 8 = = 1.2. So the discount is £1.20

£8 − £1.20 = £6.80

Alternatively the actual amount can be calculated in another way, as follows:

(100% − 15%) of £8 is 85% of £8.

85% of £8 = £(0.85 × 8)

= £6.80 (as before).

## Example 13

• (a) A carpet store is offering 20% off all its oriental rugs. What would the sale price be for a Chinese rug originally priced at £245?

• (b) The business fails to do well and decides to close down. It makes a further reduction on all its stock of 12%. What would the same Chinese rug be sold for now?

• (a) In the first sale the Chinese rug would cost (100% − 20%) of £245, 100% − 20% = 80%, 0.80 × £245 = £196.

• (b) In the final closing sale the rug would cost (100% − 12%) of £196 or 0.88 × £196 = £172.48.

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