| Directions: In each of these questions, one question is given followed by data in three statements I, II and III. You have to study the question and the data in statements and decide the question can be answered with data in which of the statements and mark your answer accordingly. [SBI (PO) 2011] |
| What is the rate of interest per cent per annum? |
| I. The difference between the compound interest and simple interest earned in 2 yr on the amount invested is Rs. 100. |
| II. The amount becomes Rs. 19500 in 3 yr oc. simple interest. |
| III. The simple interest accrued in. 2 yr on the same amount at the same rate of interest is Rs. 3000. |
A) I and II
B) I and III
C) II and III
D) I and either II or HI
E) None of these
Correct Answer: B
Solution :
| Let the amount and rate of interest be P and R, respectively. From statement I, |
| Difference in CI and SI |
| \[100=\left[ P{{\left( 1+\frac{R}{100} \right)}^{2}}-P \right]-\frac{2PR}{100}\] |
| \[\Rightarrow \]\[100=P\left[ {{\left( \frac{100+R}{100} \right)}^{2}}-P \right]-\frac{2PR}{100}\] |
| \[\Rightarrow \]\[100=P\left[ \frac{{{(100)}^{2}}+{{(R)}^{2}}+200R-{{(100)}^{2}}}{{{(100)}^{2}}} \right]-\frac{2PR}{100}\] |
| \[\Rightarrow \]\[100=PR\left[ \frac{R+200}{{{(100)}^{2}}} \right]-\frac{PR}{50}\] (i) |
| From statement III, |
| \[\frac{2PR}{100}=3000\] |
| \[\Rightarrow \] \[PR=15000\] |
| Now, putting the value of PR in Eq (i), we get |
| \[100=15000\left[ \frac{R+200}{{{(100)}^{2}}} \right]-\frac{15000}{50}\]\[[\because PR=15000]\] |
| \[\Rightarrow \]\[100=\frac{15000}{100\times 100}[R+200]-300\] |
| \[\Rightarrow \]\[100=1.5R+300-300\] |
| \[\Rightarrow \]\[R=\frac{100}{1.5}=\frac{200}{3}=66\frac{2}{3}\]% per annum |
| Hence, we will get the required percentage with statements I and III. |
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