# The Value of a Car Depreciated by 10% in the First 2 Years and by 8% in the Third Year. Express the Total Depreciation of the Car as a Single per Cent During the Three Years. - Mathematics

Sum

The value of a car depreciated by 10% in the first 2 years and by 8% in the third year. Express the total depreciation of the car as a single per cent during the three years.

#### Solution

Let value of car be Rs x.

"V"_0 =Rs x ; n = 3 ; r = 10%  for first 2 years and 8% for 3rd year .

therefore "V"_"t" = "V"_0 xx (1 - "r"/100)^"n"

=> "V"_"t" = "Rs"  "x"  xx (1 - 10/100)^2 (1 - 8/100)

=> "V"_"t" = "Rs"  "x"  xx 9/10 xx 9/10 xx 23/25

=> "V"_"t" = "Rs"  "x"  xx 1863/2500

=> "V"_"t" = "Rs"  0.7452  "x"

Depreciation in the value of car

= Rs (x - 0.7452 x) = Rs 0.2548 x

Percentage change in depreciation

= (0.2548  "x")/"x" xx 100

= 25.48 %

Percentage change = 25.48 %

Concept: Concept of Compound Interest - Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
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#### APPEARS IN

Frank ICSE Class 10 Mathematics Part 2
Chapter 1 Compound Interest
Exercise 1.3 | Q 10 | Page 10