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:
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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