The price of a product is decreased by x% and then increased by x%. The final price becomes 10% less than the original. What is the value of x (approximately)?
31.6
When a price is decreased by x% and then increased by x%, the net effect is given by \(\frac{(100-x)(100+x)}{100^2} = \frac{100 - 10}{100}\) since the final price is 10% less than original.
This gives \(\frac{10000-x^2}{10000} = 0.9\), so \(10000 - x^2 = 9000\).
Solving, \(x^2 = 1000\), so \(x = \sqrt{1000} \approx 31.6\).
Hence, the answer is 31.6.
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