Quantitative Aptitude Ques 1609

Question: A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 yr and that of 2 yr is 25: 8. The rate of interest per annum is

Options:

A) 10%

B) 11%

C) 12%

D) $ 12,\frac{1}{2} $

Show Answer

Answer:

Correct Answer: D

Solution:

  • [d] Let the principal be Rs. P and rate of interest by R% per annum. $ =[ P\times {{( 1+\frac{R}{100} )}^{2}}-P ]-( \frac{P\times R\times 2}{100} )=\frac{PR^{2}}{10^{4}} $ Difference of CI and SI for 2 yr $ =[ P\times {{( 1+\frac{R}{100} )}^{3}}-P ]-( \frac{P\times R\times 3}{100} )=\frac{PR^{2}}{10^{4}}( \frac{300+R}{100} ) $
    $ \therefore $ $ \frac{\frac{PR^{2}}{10^{4}}( \frac{300+R}{100} )}{\frac{PR^{2}}{10^{4}}}=\frac{25}{8} $

$ \Rightarrow $ $ ( \frac{300+R}{100} )=\frac{25}{8} $

$ \Rightarrow $ $ R=\frac{100}{8}=12\frac{1}{2} $ %

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