Quantitative Aptitude Ques 1741

Question: A sum of money placed at compound interest doubles itself in 4 yr. In how many years will it amount to four times itself?

Options:

A) 12 yr

B) 13 yr

C) 8 yr

D) 16 yr

Show Answer

Answer:

Correct Answer: C

Solution:

  • Let $ A=2x, $ Then, $ P=x. $ So, $ \frac{A}{P}=2 $ We know that, $ A=P{{( 1+\frac{r}{100} )}^{t}} $

$ \Rightarrow $ $ \frac{A}{P}={{( 1+\frac{r}{100} )}^{4}} $

$ \Rightarrow $ $ 2={{( 1+\frac{r}{100} )}^{4}} $ On squaring both sides, we get $ 2^{2}={{( 1+\frac{r}{100} )}^{8}} $

$ \Rightarrow $ $ 4={{( 1+\frac{r}{100} )}^{8}} $

$ \therefore $ It will become 4 times itself in 8 yr. Alternate Method If a certain sum, at compound interest becomes x time in $ t _1yr $ and $ y $ times in $ t _2yr. $ Then, $ {x^{\frac{1}{t _1}}}={y^{\frac{1}{t _2}}} $ Given, $ t _1=4yr, $ $ x=2, $ $ t _2=? $ and $ y=4 $

$ \Rightarrow $ $ {{(2)}^{1/4}}={{(4)}^{1/t _2}} $

$ \Rightarrow $ $ {{(2)}^{1/4}}={{(2)}^{2/t _2}} $ On comparing both sides, we get $ \frac{2}{t _2}=\frac{1}{4} $

$ \therefore $ $ t _2=8yr $