# The Value of a Machine Depreciates by 10%, 12% and 15% in the First 3 Years. Express the Total Depreciation of the Machine as a Single per Cent During the Three Years. - Mathematics

Sum

The value of a machine depreciates by 10%, 12% and 15% in the first 3 years. Express the total depreciation of the machine as a single per cent during the three years.

#### Solution

Let value of machine be Rs x.
Vo =Rs x ; n = 3 ; r = 10% for first year, 12 % for 2nd year and 15 %  for 3rd year

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

=> "V"_"t" = "Rs"  "x"  xx (1 - 10/100) (1 - 12/100) (1 - 15/100)

=> "V"_"t" = "Rs"  "x" xx 9/10 xx 22/25 xx 17/20

=> "V"_"t" = "Rs"  "x" xx 3366/5000

⇒ Vt = Rs. 0. 6 732x
Depreciation in the value of car

= Rs (x - 0.6732 x) =Rs 0.3268 x

Percentage change in depreciation

= (0.3268 "x")/"x" xx 100

= 32.68 %

Percentage change = 32.68 %

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 11 | Page 10