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6.Interest
medium
If the compound interest on a certain sum of money for $2$ years is $Rs. 164$ whereas the simple interest for $3$ years at the same rate is $Rs. 240$ on the same sum, find the sum (In $Rs.$)
A
$1200$
B
$1400$
C
$1600$
D
$1800$
Solution
Here, SI for 3 years $=$ Rs. 240 SI for 1 year $=$ Rs. $\frac{240}{3}$
SI for 2 years $=$ Rs. $\frac{240}{3} \times 2=$ Rs. 160 $\Rightarrow 160=\frac{ P \times R \times 2}{100} \Rightarrow PR =8000$
Hence, $(164-160)= P \left(\frac{ R }{100}\right)^{2}$
$\Rightarrow 4= P \left[\frac{8000}{ P \times 100}\right]^{2} \Rightarrow 4=\frac{ P \times 8000 \times 8000}{ P ^{2} \times(10000)}$
$\Rightarrow P = Rs .1600$
Standard 13
Quantitative Aptitude
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