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)?
Solution :
Decrease in price = x%
Increase in price = x%
Final price = 10% less than original
Formula Used:
Successive percentage change = a + b + (a × b ÷ 100)
Calculation:
First change = −x%
Second change = +x%
Net percentage change = −x + x + (−x × x ÷ 100)
Net percentage change = −x² ÷ 100
Final price is 10% less ⇒ Net change = −10
So,
−x² ÷ 100 = −10
x² ÷ 100 = 10
x² = 1000
x = √1000
x = 31.6228
x ≈ 31.6%
Therefore, the correct answer is 31.6%.