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?
Answer
(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.