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6.Interest
medium
If the compound interest on a sum for $2$ years at $12 \frac{1}{2} \%$ per annum is ₹ $510,$ the simple interest (In ₹) on the same sum at the same rate for the same period of time is.
A
$400$
B
$450$
C
$460$
D
$480$
Solution
Let the principal amount be $P$.
$\therefore \quad P\left[\left(1+\frac{12(1 / 2)}{100}\right)^{2}-1\right]=₹ 510$
i.e. $\quad P\left[\left(1+\frac{1}{8}\right)^{2}-1\right]=510$
i.e. $P\left[\left(\frac{9}{8}\right)^{2}-1\right]=510$
Or $P=\frac{510 \times(8)^{2}}{(9)^{2}-(8)^{2}}=\frac{510 \times(8)^{2}}{(9+8) \times 1}=30 \times 64=₹ 1920$
$\therefore \quad$ S.I. $=1920 \times 2 \times \frac{25}{200}=₹ 480$
Standard 13
Quantitative Aptitude
