| Directions: In each of the following questions, a question followed by two statements numbered I and II are given. You are to read both the statements and then give answers. |
| What is the rate of interest per cent per annum? |
| I. An amount of Rs. 6200 fetches simple interest of Rs. 1736 in 2 yr. |
| II. An amount of Rs. 4500 fetches compound interest of Rs. 1348.20 in 2 yr. |
A) If the data given in statement I alone are sufficient to answer the question whereas the data given in statement II alone are not sufficient to answer the question
B) If the data given in statement II alone are sufficient to answer the question whereas the data given in statement I alone are not sufficient to answer the question
C) If the data in either statement I alone or in statement II alone are sufficient to answer the questions.
D) If the data in both the statements I and II are not sufficient to answer the question
E) If the data given in both the statement I and II are necessary to answer the question
Correct Answer: C
Solution :
| From statement I, |
| \[R=\frac{SI\times 100}{P\times T}\]\[\Rightarrow \]\[\frac{1736\times 100}{6200\times 2}\] |
| = 14% |
| From statement II, \[CI=P{{\left( 1+\frac{r}{100} \right)}^{2}}-P\] |
| \[\Rightarrow \]\[1348.2=4500{{\left( 1+\frac{r}{100} \right)}^{2}}-4500\] |
| \[\Rightarrow \]\[1348.2+4500=4500{{\left( 1+\frac{r}{100} \right)}^{2}}\] |
| \[\Rightarrow \]\[5848.2=4500{{\left( 1+\frac{r}{100} \right)}^{2}}\] |
| \[\Rightarrow \]\[\frac{58482}{45000}={{\left( 1+\frac{r}{100} \right)}^{2}}\]\[\Rightarrow \]\[\frac{3249}{2500}={{\left( 1+\frac{r}{100} \right)}^{2}}\] |
| \[\Rightarrow \]\[{{\left( \frac{57}{50} \right)}^{2}}={{\left( 1+\frac{r}{100} \right)}^{2}}\]\[\Rightarrow \]\[1+\frac{r}{100}=\frac{57}{50}\] |
| \[\Rightarrow \]\[\frac{r}{100}=\frac{57}{50}-1=\frac{7}{50}\]\[\Rightarrow \]\[r=\frac{7\times 100}{50}\] |
| \[\therefore \] \[r=14\]% |
| Both statements are alone sufficient. |
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