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6.Interest
medium
If the compound interest on a certain sum for $2$ $years$ at $3 \%$ per annum is $Rs. 101.50$ , then the simple interest (In $Rs.$) on the same sum at the same rate and for the same time will be
A
$90.00$
B
$95.50$
C
$100.00$
D
$98.25$
Solution
Let the sum be Rs. P. By the Formula
$\Rightarrow CI = P \left[\left(1+\frac{ r }{100}\right)^{ t }-1\right] \Rightarrow 101.50= P \left[\left(1+\frac{3}{100}\right)^{2}-1\right]$
$\Rightarrow 101.50= P \left[\left(\frac{103}{100}\right)^{2}-1\right] \Rightarrow 101.50= P \left(\frac{10609-10000}{10000}\right)$
$\Rightarrow P=\frac{101.50 \times 10000}{609}=R s . \frac{1015000}{609}$
$\therefore \quad SI =\frac{1015000 \times 2 \times 3}{609 \times 100}= Rs .100$
Standard 13
Quantitative Aptitude
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