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
$ \Rightarrow $ $ 100=P[ {{( \frac{100+R}{100} )}^{2}}-P ]-\frac{2PR}{100} $
$ \Rightarrow $ $ 100=P[ \frac{{{(100)}^{2}}+{{(R)}^{2}}+200R-{{(100)}^{2}}}{{{(100)}^{2}}} ]-\frac{2PR}{100} $
$ \Rightarrow $ $ 100=PR[ \frac{R+200}{{{(100)}^{2}}} ]-\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[ \frac{R+200}{{{(100)}^{2}}} ]-\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.
BETA
