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6.Interest
medium
The simple interest on a certain sum of money for $3$ years at $8 \%$ per annum is half the compound interest on ₹ $4000$ for $2$ years at $10 \%$ per annum. The sum placed on simple interest (In ₹) is
A
$1550$
B
$1650$
C
$1750$
D
$2000$
Solution
Let the sum be $P$.
S.I. for 3 years $=\frac{P \times 3 \times 8}{100}$
C.I. (for $₹ 4000 @ 10 \%$ p.a for 2 year $)=4000\left(1+\frac{10}{100}\right)^{2}-4000$
$=4000\left[\left(\frac{11}{10}\right)^{2}-1\right]=4000 \times\left(\frac{11^{2}-10^{2}}{10^{2}}\right)$
$=40 \times 21=840$
$\therefore \quad$ From (1) and (2)
$P \times \frac{3 \times 8}{100}=\frac{1}{2} \times C.I. =\frac{1}{2} \times 840=420$
$P=\frac{420 \times 100}{24}=70 \times 25=₹ 1750$
Standard 13
Quantitative Aptitude
