A shopkeeper offers his goods under four schemes, each of two successive discounts. Which scheme is the most beneficial for the customer?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 16% and 4%
Two successive discounts of \(a\%\) and \(b\%\) equal a single discount of \(\displaystyle \left(a+b-\frac{ab}{100}\right)\%\). In every scheme \(a+b=20\), so the scheme with the smallest product \(ab\) gives the largest discount.
10% and 10%: \(\displaystyle 20-\frac{100}{100}=19\%\)
15% and 5%: \(\displaystyle 20-\frac{75}{100}=19.25\%\)
12% and 8%: \(\displaystyle 20-\frac{96}{100}=19.04\%\)
16% and 4%: \(\displaystyle 20-\frac{64}{100}=19.36\%\)
The largest single discount, 19.36%, comes from the scheme of 16% and 4%.