Discussion
If successive discounts are 10%, 20% and 30%, then what is its single equivalent discount?
Answer: C
Multiply the three retained fractions.
\[ (1-0.10)(1-0.20)(1-0.30) = 0.90 \times 0.80 \times 0.70 \]
\[ 0.90 \times 0.80 = 0.72, \qquad 0.72 \times 0.70 = 0.504 \]
\[ \text{single equivalent discount} = 1 - 0.504 = 0.496 = 49.6\% \]
Adding the rates gives 60%, well above the truth, because each later discount acts on a smaller base. Chaining discounts can never reach 100% however many are applied.
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