| 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 [SSC (CGL) 2011] |
A) Rs.1000
B) Rs. 1200
C) Rs. 1500
D) Rs. 2000
Correct Answer: B
Solution :
| Given, \[CI-SI=Rs.\,48\] and r = 20% |
| We know that, \[SI=\frac{P\times r\times t}{100}\] |
| and \[CI=P\left[ {{\left( 1+\frac{r}{100} \right)}^{t}}-1 \right]\] |
| Then, according to the question, |
| \[P\left[ {{\left( 1+\frac{r}{100} \right)}^{t}}-1 \right]-\frac{P\times r\times t}{100}=48\] |
| \[\Rightarrow \]\[\left[ {{\left( 1+\frac{20}{100} \right)}^{2}}-1 \right]-\frac{P\times 20\times 2}{100}=48\] |
| \[\Rightarrow \] \[P\left[ {{\left( \frac{6}{5} \right)}^{2}}-1 \right]-\frac{2P}{5}=48\] |
| \[\Rightarrow \] \[P\left[ \frac{36}{25}-1 \right]-\frac{2P}{5}=48\] |
| \[\Rightarrow \] \[\frac{11\,\,P}{25}-\frac{2\,\,P}{5}=48\] |
| \[\Rightarrow \] \[\frac{11\,\,P-10\,\,P}{25}=48\] |
| \[\therefore \] P = Rs. 1200 |
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