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
