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- Quantitative Aptitude
If the compound interest on a sum for $2$ years at $12 \frac{1}{2} \%$ per cent is ₹ $510$, the simple interest (In ₹) on the same sum at the same rate for same period of time is
$400$
$450$
$460$
$480$
Solution
(d) Let the principal be ₹P.
$\therefore \quad CI =P\left[\left(1+\frac{R}{100}\right)^{T}-1\right]$
$\Rightarrow \quad 510=P\left[\left(1+\frac{\frac{25}{2}}{100}\right)^{2}-1\right]$
$\Rightarrow \quad 510=P\left[\left(1+\frac{1}{8}\right)^{2}-1\right]$
$\Rightarrow \quad 510=P\left[\left(\frac{9}{8}\right)^{2}-1\right]$
$\Rightarrow \quad 510=P\left(\frac{81}{64}-1\right)$
$\Rightarrow \quad 510=P\left(\frac{81-64}{64}\right)=\frac{17 P}{64}$
$\Rightarrow \quad P=\frac{510 \times 64}{17}=₹ 1920$
$\therefore \quad SI =\frac{\text { Principal } \times Time \times Rate }{100}$
$=\frac{1920 \times 2 \times 25}{100 \times 2}=₹ 480$
