Question : A tradesman marks his goods at 25% above the cost price. If he reduces the marked price by $12\frac{1}{2}\%$, then his profit will be:
Option 1:
$9\frac{3}{8}\%$
Option 2: $7\frac{3}{5}\%$
Option 3: $6\frac{3}{8}\%$
Option 4: $5\frac{1}{3}\%$
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Correct Answer:
$9\frac{3}{8}\%$
Solution :
Use the successive percentage change formula, where $x$ and $y$ are percentage increases or decreases, if increases take positive and if decreases take negative.
$=(x+y+\frac{xy}{100})\%$
We have, $x = 25\%$ and $y=-12\frac{1}{2}\%=-\frac{25}{2}\%$
The required profit percentage,
$=(25-\frac{25}{2}-\frac{25×25}{200})\%$
$=(25-\frac{25}{2}-\frac{25}{8})\%$
$=\frac{75}{8}\%$
$=9\frac{3}{8}\%$
Hence, the correct answer is $9\frac{3}{8}\%$.
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