A single discount equivalent to three successive discounts of \(22\frac{2}{9}\)%, \(14\frac{2}{7}\)% and \(6\frac{1}{4}\)% is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 37.5%
Successive discounts are multiplied, not added: after each discount the buyer pays a fraction of the price left. These three rates are simple fractions.
\(\displaystyle 22\frac{2}{9}\%=\frac{2}{9}\), so the buyer pays \(\displaystyle \frac{7}{9}\)
\(\displaystyle 14\frac{2}{7}\%=\frac{1}{7}\), so the buyer pays \(\displaystyle \frac{6}{7}\)
\(\displaystyle 6\frac{1}{4}\%=\frac{1}{16}\), so the buyer pays \(\displaystyle \frac{15}{16}\)
Fraction paid after all three \(\displaystyle =\frac{7}{9}\times\frac{6}{7}\times\frac{15}{16}=\frac{5}{8}\)
Single discount \(\displaystyle =1-\frac{5}{8}=\frac{3}{8}=37.5\%\)
The equivalent single discount is 37.5%.