Quantitative Aptitude Ques 2144

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