Three equal successive discounts on an article are equivalent to a single discount of 48.8%. Find each discount.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 20%
Successive discounts multiply: after a discount of \(d\%\) the buyer pays \(\left(1-\frac{d}{100}\right)\) of the price, and after three equal discounts he pays the cube of that.
Single discount 48.8%, so the buyer pays \(100-48.8=51.2\%\) of the marked price
\(\displaystyle \left(1-\frac{d}{100}\right)^{3}=0.512\)
\(0.512=0.8^{3}\), so \(\displaystyle 1-\frac{d}{100}=0.8\)
\(d=20\)
Check: \(0.8\times0.8\times0.8=0.512\), a total discount of 48.8%
Each discount is 20%.