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- Quantitative Aptitude
The difference between the simple interest on a certain sum at the rate of $10 \%$ per annum for $2$ years and compound interest which is compounded every $6$ months is ₹ $124.05$ . What is the principal (In ₹) ?
$6000$
$8000$
$10000$
$12000$
Solution
Let $P$ be the principal.
S.I. on first year $=P \times \frac{10 \times 1}{100}=\frac{P}{10}$
S.I. on second year $=P \times \frac{10 \times 1}{100}=\frac{P}{10}$
Total S.I. $=2 \times \frac{P}{10}=\frac{P}{5}$
C.I. for 2 year $=P\left(1+\frac{R}{200}\right)^{4}-P$
$=P\left[\left(1+\frac{10}{200}\right)^{4}-1\right]$
$=P\left[\left(1+\frac{5}{100}\right)^{4}-1\right]$
$(2)-(1) \Rightarrow P\left[\left(1+\frac{5}{100}\right)^{4}-1-\frac{1}{5}\right]=124.05$
$P\left[\left(\frac{21}{20}\right)^{4}-\frac{6}{5}\right]=124.05$
Or $P\left[\frac{1,94,481}{1,60,000}-\frac{6}{5}\right]=124.05$
Or $P=\frac{12405}{100} \times \frac{1,60,000}{1,94,481-1,92,000}$
$=₹ 8000$
