If the selling price of an item is increased by 25% and the profit also increases from 20% to 30%, what is the percentage increase in the cost price?
15.38%
Let the original cost price be C. With 20% profit, original selling price = 1.2C.
New selling price = 1.25 × 1.2C = 1.5C.
Let the new cost price be C′. With 30% profit, new selling price = 1.3C′.
\(1.3C' = 1.5C \Rightarrow C' = \frac{1.5}{1.3}C = \frac{15}{13}C \approx 1.1538C\).
Increase in cost price = \(\frac{15}{13} - 1 = \frac{2}{13} \approx 15.38\%\).
Hence, the cost price increases by about 15.38%.
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