The price of a machine got depreciated by 50% in the 1st year, $33\frac{1}{3}$% in the 2nd year and 25% in the 3rd year. Overall, by how much has the machine depreciated?

75%

Let initial price = 100x

Price after depreciation = \(\frac{50}{100}\) × 33\(\frac{1}{3}\) ×  \(\frac{25}{100}\) × 100x

= \(\frac{1}{2}\) × \(\frac{2}{3}\) ×  \(\frac{3}{4}\) × 100x

= 25x

Required percentage = \(\frac{100x - 25x }{100x}\) × 100 = 75%