Question

The value of a refrigerator depreciates by 8% of its value at the beginning of the year. Find the original value of the refrigerator if it depreciated by Rs 2,392 in the second year.

Answer 1

Let value of the refrigerator be Rs x. 

V_o =Rs x ; n = 2 ; r = 8 % 

Depreciation in the first year = 

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

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

`=> "V"_"t" = "Rs"  "x"  xx 23/25`

`=> "V"_"t" = "Rs"  0.92  "x"`

Depreciation in the second year = 

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

`=> "V"_"t" = "Rs"  0.92  "x" xx (1- 8/100)`

`=> "V"_"t" = "Rs"  0.92  "x"  xx 23/25`

`=> "V"_"t" = "Rs"  0.8464  "x" `

Depreciation in the value of refrigerator in the second year 
= Rs (0.92 x-0.8464 x) =Rs 2,392 
⇒ 0.0736 x = Rs 2,392 
⇒ x = Rs 32,500 
The original value of the refrigerator was Rs 32,500.