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# A TV was bought at a piece of Rs.$\,21000$. After one year the value of the TV was depreciated by $5\%$. (Depreciation means reduction of value due to use and age of the item). Find the value of the TV after one year.

Last updated date: 12th Aug 2024
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Hint:Depreciation refers to when the value of something goes down over time.
Depreciation $\%$ occurring on cost price is formulated as:
Reduced amount of after depreciation is formulated as
Initial Cost Price $-$ Depreciation $=$ Reduced Cost Price.

Complete step by step solution:
Given,
Initial Cost Price of T.V. $=$Rs.$21000$ ……. (i)
Depreciation $\%$after one year $= 5\%$ ……… (ii)
We know that the Depreciation occurs at Cost Price.
Hence,
Depreciation $\%$ of Cost Price $=$ Depreciated amount
Put value from (i) and (ii)
We get,
Depreciated amount $= 5\% \,of\,2100$
$= \dfrac{5}{{100}} \times \,2100\,$ $\,[\because 5\% = \dfrac{5}{{100}}]$
$= 5 \times 210$
Depreciated amount $= Rs.\,1050$ ………. (iii)
Reduced Cost Price of the product must be equal to:
Reduced Cost Price $=$ Initial Cost Price $-$ Depreciated amount
Using Value from (i) and (iii)
Reduced Cost Price
$= Rs.\,21000 - Rs.\,1050$
$= Rs.\,(21000 - \,1050)$
$= Rs.\,19950$
Hence, the value of the T.V after one year $= Rs.\,19950$

Note:Never confuse Depreciation with Discount.
Depreciation as mentioned in the question is reduction in price of an item due to use and age of the item. Whereas, Discount is the amount offered to a customer by the seller on a new item.