Lata buys a second-hand scooty for ₹30,000. The value of the scooty depreciates at the rate of x% yearly. If the scooty was sold at a price of ₹20,667 after 2 years, then what is the value of x?

Correct option is C

Given:

Initial value (P) = ₹30,000

Value after 2 years = ₹20,667

Depreciation rate = x% per year

Need: Value of x.

Formula Used:

Depreciation formula (compound):

Value after n years = P $$\times \left(1 - \frac{x}{100}\right)^n$$​

Solution:

Here,

20667 = 300$$00 \times \left(1 - \frac{x}{100}\right)^2$$​

​$$\left(1 - \frac{x}{100}\right)^2 = \frac{20667}{30000}$$​

​$$\left(1 - \frac{x}{100}\right)^2 = 0.6889$$​

Taking square root:

​$$1 - \frac{x}{100} = \sqrt{0.6889}$$​

​$$1 - \frac{x}{100} = 0.83$$​

​$$\frac{x}{100} =$$​ 1 - 0.83 = 0.17

x = 17

Final Answer:

17% per annum depreciation