Quantitative Aptitude Ques 1452
Question: On what sum does the difference between the compound interest and the simple interest for 3 yr at 10% is Rs. 31?
Options:
A) Rs. 1500
B) Rs. 1200
C) Rs. 1100
D) Rs. 1000
Show Answer
Answer:
Correct Answer: D
Solution:
- Let the sum be Rs. $ x. $ $ r=10 $ %and $ t=3yr $ $ SI=\frac{x\times r\times t}{100} $ $ SI=\frac{x\times 10\times 3}{100}=\frac{3}{10}x $ $ CI=[ {{( 1+\frac{r}{100} )}^{t}}-1 ]x=[ {{( 1+\frac{10}{100} )}^{3}}-1 ]x $ $ =[ {{( \frac{11}{10} )}^{3}}-1 ]x=( \frac{1331}{1000}-1 )x=\frac{331}{1000}x $ According to the question, $ CI-SI=31 $
$ \Rightarrow $ $ \frac{331}{1000}x-\frac{3}{10}x=31 $
$ \Rightarrow $ $ \frac{(331-300)}{1000}x=31 $
$ \Rightarrow $ $ \frac{31}{1000}x=31 $
$ \therefore $ $ x=1000 $
$ \therefore $ $ Sum=Rs\text{. 1000} $ Alternate Method When difference between the CI and SI on a certain sum of money for 3 yr at r % rate is Rs. x, then Difference between SI and CI $ =\frac{{{\Pr }^{2}}(300+r)}{{{(100)}^{3}}} $
$ \Rightarrow $ $ 31=\frac{P\times {{(10)}^{2}}(300+10)}{1000000} $
$ \Rightarrow $ $ 31=\frac{P\times 100\times 310}{1000000} $
$ \Rightarrow $ $ 31=\frac{31P}{1000} $
$ \Rightarrow $ $ P=1000. $
BETA
