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The production cost of an item increased by $20\%$ and the government also started taxing the item $20\%$ on the selling price in addition to a $2.5$ units fixed charge. If the initial cost price is $100$ units, the percentage increase in the selling price which will ensure profit remains the same would be ____
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Original CP $=100$

Profit $= y-100$.

New, CP $=120$.

New, SP, $y' = 120 + 0.2y' + (y-100) – 2.5$ because profit remains the same and not the profit percentage

$\implies y' = \frac{y+20}{0.8} – 2.5 = 1.125 y$

So, CP must increase by $12.5\%$ to retain the same profit.
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