The price of a bike is firstly decreased by 25 percent and then increased by 50 percent. What is the percentage increase in the price of bike?

The price of a bike is first decreased by 25%, then increased by 50%.

When successive percentage changes are applied, the final effect can be calculated by applying each change sequentially.

A decrease of x% followed by an increase of y% results in an overall percentage change given by:

​$$\text{Net Percentage Change} = x + y + \frac{x \cdot y}{100}$$​​

take x = −25% and y = 50%

$$\text{Net Percentage Change} = −25+50+\frac{(-25)\times50}{100}\\=-25 + 50 - \frac{1250}{100}\\ \ \\=−25+50−\frac{1250}{100}\\ \ \\ =25−12.5\\ \ \\= 25 - 12.5\\ \ \\=12.50$$