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The Value of a Scooter Depreciates by 12% of Its Value at the Beginning of the Year. Find the Original Value of the Scooter If It Depreciated by Rs 2,640 in the Second Year. - Mathematics

Sum

The value of a scooter depreciates by 12% of its value at the beginning of the year. Find the original value of the scooter if it depreciated by Rs 2,640 in the second year.

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Solution

Let value of the soooter be Rs x. 

Vo =Rs x ; n = 2 ; r = 12 % 

Depreciation in the first year = 

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

`=> "V"_"t" = "Rs"  "x" xx (1 - 12/100)`

`=> "V"_"t" ="Rs"  "x" xx 22/25 `

`=> "V"_"t" = "Rs"  0.88  "x"`

Depreciation in the second year = 

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

`=> "V"_"t" = "Rs"  0.88  "x" xx (1 - 12/100)`

`=> "V"_"t" ="Rs"   0.88  "x" xx 22/25 `

`=> "V"_"t" = "Rs"  0.7744  "x"`

Depreciation in the value of soooter in the second year 

=Rs (0.88 x - 0.7744 x) =Rs 2,640 
⇒  0.1056 x = Rs 2,640 
⇒  x =Rs 25,000 
The original value of the soooter was Rs 25,000. 

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 12 | Page 10
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