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6.Interest
medium
If the compound interest on a certain sum for $3$ years at $5 \%$ p.a exceeds the simple interest on the same sum and for the same time and at the same rate by $Rs. 183,$ find the sum. (In $Rs.$)
A
$17560$
B
$21680$
C
$24000$
D
$26780$
Solution
According to the question $\Rightarrow CI – SI =183$
Here, $SI =\frac{ P \times 5 \times 3}{100}=\frac{3 P }{20}$
$\Rightarrow \quad C I=P\left[\left(1+\frac{5}{100}\right)^{3}-1\right]=P\left[\left(\frac{21}{20}\right)^{3}-1\right]=P\left[\frac{1261}{8000}\right]$
Putting values of
(ii) and (iii) in (i):
$\Rightarrow \frac{1261}{8000} P -\frac{3 P }{20}=183 \Rightarrow \frac{1261 P }{8000}-\frac{1200 P }{8000}=183$
$\Rightarrow 61 P=183 \times 8000 \Rightarrow P=R s .24000$
Standard 13
Quantitative Aptitude
