Q.2. The value of an article decreased for two years at the rate of 10 % per year and then in the third year it increased by 10 %. Find the original value of the article, if its value at the end of 3 years is Rs. 40,095.

Dear Student,

Please find below the solution to the asked query:

Let , Original value of article =  P 

And we know formula when price decreased :  Amount =  P${\left(1 - \frac{r}{100}\right)}^t$

Here , r  = 10  and t  = 2 ( In years )  , So

Value of the article after 2 years  =  P${\left(1 - \frac{10}{100}\right)}^2 =P{\left(1 - \frac{1}{10}\right)}^2=P{\left(\frac{9}{10}\right)}^2=P\left(\frac{81}{100}\right) = \frac{\mathbf{81}\mathbf{ }\mathbf{P}}{\mathbf{100}}$

Also given : In third year value is increased by 10 %  , So 

Value of article after three years  = $\frac{81 P}{100}+10\%of\frac{{\displaystyle 81 P}}{{\displaystyle 100}} = \frac{{\displaystyle 81 P}}{{\displaystyle 100}}+\frac{{\displaystyle \frac{{\displaystyle 81 P}}{{\displaystyle 100}} \times 10}}{100} = \frac{{\displaystyle 81 P}}{{\displaystyle 100}}+\frac{{\displaystyle \frac{{\displaystyle 81 P}}{{\displaystyle 10}}}}{100}= \frac{{\displaystyle 81 P}}{{\displaystyle 100}}+\frac{{\displaystyle 81 P}}{1000} \frac{{\displaystyle 810 P + 81 P}}{{\displaystyle 1000}} = \frac{{\displaystyle 891 P}}{\mathbf{1000}}$

Also given value of article after three years  =  Rs . 40095  , So

$$\begin{gathered} \frac{891 P}{1000} = 40095 \\ \Rightarrow P = 40095 \times \frac{1000}{891} \\ \Rightarrow P = 45 \times 1000 \\ \mathbf{\Rightarrow }\mathit{P}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{45000} \end{gathered}$$
Therefore,

Original value of article = Rs. 45000                                                     ( Ans )


Hope this information will clear your doubts about topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards