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- Standard 13
- Quantitative Aptitude
A sum of $Rs. 1000$ after $3 \,years$ at compound interest becomes a certain amount that is equal to the amount that is the result of a $3 \,year$ depreciation from $Rs. 1728$. Find the difference between the rates (In $\%$) of $C.I.$ and depreciation? (Given $C.I.$ is $10 \%$ $p.a.$)
$1.7$
$2.9$
$4$
$7.6$
Solution
The amount of Rs. 1000 at $10 \%$ p.a. after 3 years would becomes:
$\Rightarrow P\left(1+\frac{R}{100}\right)^{3}=A \Rightarrow 1000\left(1+\frac{10}{100}\right)^{5}=A$
$\Rightarrow A=R s .1331$
Here, now the principal of Rs. 1728 depreciated at rate of $R \%$ per annum and amounts to Rs. 1331
$\Rightarrow P\left[\left(1-\frac{R}{100}\right)\right]^{3}=1331$
$\Rightarrow 1728\left[\left(1-\frac{ R }{100}\right)\right]^{3}=1331$
$\Rightarrow\left(1-\frac{ R }{100}\right)^{3}=\frac{1331}{1728} \Rightarrow 1-\frac{ R }{100}=\frac{11}{12}$
$\Rightarrow \frac{ R }{100}=\frac{1}{12}$ or $R =8.33 \%$
$\Rightarrow$ Hence rate difference between CI and $\quad$ depreciation is almost $=(10-8.33) \%=1.7$
