High School

Ex. (2) Rehana purchased a scooter in the year 2015 for ₹60000. If its value falls by 20% every year, what will be the price of the scooter after 2 years?

Answer :

To determine the price of the scooter after 2 years, we can follow a step-by-step method using the concept of depreciation. Depreciation is a decrease in the value of an asset over time, and this problem demonstrates a constant rate of depreciation.

  1. Initial Value: Rehana purchased the scooter for ₹60,000 in the year 2015. This is our starting value for the calculation.

  2. Depreciation Rate: The value of the scooter falls by 20% every year. This means that after each year, the scooter retains only 80% of its value from the previous year (because 100% - 20% = 80% or 0.8 as a decimal).

  3. Calculate Value After 1 Year:

    • The value of the scooter after the first year can be calculated as:

      [tex]\text{Value after Year 1} = \text{Initial Value} \times (1 - \text{Depreciation Rate})[/tex]

      [tex]\text{Value after Year 1} = 60,000 \times 0.8 = 48,000[/tex]

    So, after the first year, the scooter's value is ₹48,000.

  4. Calculate Value After 2 Years:

    • To find the value after the second year, apply the depreciation percent again:

      [tex]\text{Value after Year 2} = \text{Value after Year 1} \times 0.8[/tex]

      [tex]\text{Value after Year 2} = 48,000 \times 0.8 = 38,400[/tex]

    Therefore, the value of the scooter after 2 years will be ₹38,400.

This method allows us to see how the scooter loses 20% of its value each year, applying the same percentage decrease successively over the years in question.