Question

A person purchases a television set for $Rs.16000$. Its life is estimated to be $20$ years. If the yearly depreciation is assumed to be constant, Find the rate of depreciation and the price after $8$ years?

Answer 1

In this question we need to find the rate of depreciation of the television set and its price after $8$ years. As it is given that in the question the life of the television set is $20$ years and the cost at which the person purchases it is $Rs.16000$ . Therefore its value would evaluate to be zero after $20$ years.

Complete step by step solution:
Here, considering the question, we have been asked to find the rate of depreciation of the television set and its price after $8$ years.
From the question it is given that the life of the television set is $20$ years and the cost at which the person purchases it is $Rs.16000$ . Therefore its value would evaluate to be zero after $20$ years.
This will form an arithmetic progression whose general term is given as ${{T}_{n}}=a+\left( n-1 \right)d$ where $a$ is the first term and $n$ is the number of the term and $d$ is the common difference.
Here the $21$ term should be zero as the estimated life is $20$ years.
Hence we can substitute the values $a=Rs.16000$ , $n=21$ and ${{T}_{n}}=0$ after that we will have
$\begin{aligned} & \Rightarrow 0=16000+\left( 21-1 \right)d \\\ & \Rightarrow 0=16000+20d \\\ & \Rightarrow 20d=-16000 \\\ & \Rightarrow d=-800 \\\ \end{aligned}$
Therefore the rate of depreciation of the price of the television set is $800$ per year.
Now as we need to find the price of the television set after $8$ years we will substitute $a=16000$ , $n=9$ and $d=-800$ after that we will have
$\begin{aligned} & \Rightarrow 16000+\left( 9-1 \right)\left( -800 \right)\\\ & \Rightarrow 16000-800\left( 8 \right) \\\ & \Rightarrow 16000-6400 \\\ & \Rightarrow 9,600Rs. \\\ \end{aligned}$

Therefore the price of the television set after $8$ years is $Rs.9,600$

Note: We should be very careful while answering questions of this type we should be sure with the calculations and concepts. We should be sure with the meaning of the word “depreciation” which means a reduction in the value of an asset over time, due in particular to wear and tear. And we should substitute $n=9$ not $8$ because we have been asked to find the price after $8$ years.