A shopkeeper allows a discount of 10% on the marked price. How much above the cost price must he mark his goods to gain 8%?

20%

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100%

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80%

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None of these

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Solution

The correct option is C 20%
let Marked price of an article be $x$
Discount on article $= x - 10$ %of $x$

$= x - \frac{10}{100} x$
$= 0.9 x$
Therefore, selling price of the article $= 0.9 x$
Now, Gain % $= \frac{s p - c p}{c p}$
Put the value of gain % and $s p$ in the above equation and calculate $c p$ .
$\frac{8}{100} = \frac{0.9 x - c p}{c p}$
$8 c p = 90 x - 100 c p$
$108 c p = 90 x$
$c p = \frac{90 x}{108}$
$c p = \frac{5 x}{6}$
Therefore, cost price $c p$ marked above marked price( $m p$ ) $= \frac{m p - c p}{c p} \times 100$
Put the valus of $c p$ and $m p$ in the above equation
$= \frac{x - \frac{5 x}{6}}{\frac{5 x}{6}} \times 100$
$= \frac{\frac{x}{6}}{\frac{5 x}{6}}$
$20$ %

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