Two successive discounts of $10\%$ and $20\%$ are equivalent to a single discount of

Two successive discounts of $10\%$ and $20\%$ are equivalent to a single discount of
  1. $28\%$
  2. $30\%$
  3. $25\%$
  4. $32\%$

Solution

Net factor $= 0.90 \times 0.80 = 0.72$, so equivalent discount $= 28\%$. Shortcut: $a + b - \dfrac{ab}{100} = 10 + 20 - 2 = 28$.

Asked in: IMO

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