A) Rs. 400
B) Rs. 800
C) Rs. 4000
D) Rs. 5000
Correct Answer: D
$ \Rightarrow $ $ P[ {{( 1+\frac{4}{100} )}^{2}}-1 ]-\frac{P\times 4\times 2}{100}=8 $
$ \Rightarrow $ $ P[ {{( \frac{26}{25} )}^{2}}-1 ]-\frac{8P}{100}=8 $
$ \Rightarrow $ $ P[ ( \frac{676}{625} )-1 ]-\frac{8P}{100}=8 $
$ \Rightarrow $ $ P[ \frac{676-625}{625} ]-\frac{8P}{100}=8 $
$ \Rightarrow $ $ \frac{51P}{625}-\frac{8P}{100}=8 $
$ \Rightarrow $ $ 5100P-5000P=500000 $
$ \Rightarrow $ $ 100P=500000 $
$ \Rightarrow $ $ P=\frac{500000}{100}=Rs\text{. 5000} $ Alternate Method When difference between the $ CI $ and $ SI $ on a certain sum of money for 2 yr at r% rate is Rs. x. Difference between $ SI $ and $ CI=\frac{Rr^{2}}{{{(100)}^{2}}} $
$ \Rightarrow $ $ 8=\frac{P\times 16}{{{(100)}^{2}}} $
$ \Rightarrow $ $ 8=\frac{16P}{10000} $
$ \Rightarrow $ $ 16P=80000 $
$ \Rightarrow $ $ P=\frac{80000}{16} $
$ \therefore $ $ P=Rs\text{. 5000} $
BETA
