Question: The difference between simple interest and compound interest of a certain sum of money a 20% per annum for 2 yr is Rs. 48. Then, the sum
Options:
A) Rs.1000
B) Rs. 1200
C) Rs. 1500
D) Rs. 2000
Show Answer
Answer:
Correct Answer: B
Solution:
- Given, $ CI-SI=Rs.,48 $ and r = 20%
We know that, $ SI=\frac{P\times r\times t}{100} $
and $ CI=P[ {{( 1+\frac{r}{100} )}^{t}}-1 ] $
Then, according to the question,
$ P[ {{( 1+\frac{r}{100} )}^{t}}-1 ]-\frac{P\times r\times t}{100}=48 $
$ \Rightarrow $ $ [ {{( 1+\frac{20}{100} )}^{2}}-1 ]-\frac{P\times 20\times 2}{100}=48 $
$ \Rightarrow $ $ P[ {{( \frac{6}{5} )}^{2}}-1 ]-\frac{2P}{5}=48 $
$ \Rightarrow $ $ P[ \frac{36}{25}-1 ]-\frac{2P}{5}=48 $
$ \Rightarrow $ $ \frac{11P}{25}-\frac{2P}{5}=48 $
$ \Rightarrow $ $ \frac{11P-10P}{25}=48 $
$ \therefore $ P = Rs. 1200