# 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.

#### 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