Find a single discount equivalent to successive discounts of $10 %$ and $20 %$ .

$18.18 %$

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$22.22 %$

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$19 %$

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$28 %$

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Solution

The correct option is D $(28 %)$

Let MP be $= R s . 100$
Given two successive discounts $d_{1}$ $= 10 %$ and $d_{2}$ $= 20 %$

$S.P = M.P \times \frac{100 - d_{1}}{100} \times \frac{100 - d_{2}}{100}$

$= 100 \times \frac{100 - 10}{100} \times \frac{100 - 20}{100}$
$= 100 \times \frac{90}{100} \times \frac{80}{100}$
$= 9 \times 8$
$= R s . 72$

$∴$ Single equivalent discount $= 100 - 72 = 28 %$

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