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- Standard 13
- Quantitative Aptitude
A sum of money at compound interest amounts in two years to Rs. $2809,$ and in three years to $Rs. 2977.54 .$ Find the rate of interest and the original sum.
$4 \,\,\%,$ $Rs. 2500$
$6 \,\,\%$ $Rs. 1800$
$4 \,\,\%,$ $Rs. 1800$
$6 \,\,\%,$ $Rs. 2500$
Solution
The difference in amount of money will determine compound interest of one year $\Rightarrow$ Hence, Rs. $[2977.54-2809]=$ Rs. 168.54
This is the CI levied on Rs. $2809,$ in one year. Hence, $CI = P \left[1+\frac{ R }{100}-1\right]$
$\Rightarrow 168.54=2809\left[\frac{ R }{100}\right] \Rightarrow \frac{16854}{2809}= R \Rightarrow R =6 \%$
The amount at CI for 2 years is:
$\Rightarrow 2809= P \left[1+\frac{6}{100}\right]^{2} \Rightarrow 2809= P \left[\frac{106}{100} \times \frac{106}{100}\right]$
$\Rightarrow P=R s .2500$
