Question: A sum of money at compound interest amounts to thrice itself in 3 yr. In how many years will it be 9 times itself?
Options:
A) 9 yr
B) 27 yr
C) 6 yr
D) 3 yr
Show Answer
Answer:
Correct Answer: C
Solution:
- Let $ A=Rs.3x, $ $ P=Rs.x $
$ \because $ $ A=P{{( 1+\frac{r}{100} )}^{t}} $
Then, $ 3x=x{{( 1+\frac{r}{100} )}^{3}} $
$ \Rightarrow $ $ 3=1{{( 1+\frac{r}{100} )}^{3}} $
On squaring both sides, we get
$ 9=1{{( 1+\frac{r}{100} )}^{6}} $
It will become 9 times itself in 6 yr
Alternate Method
If a certain sum, at compound interest becomes z times in $ t _1 $ yr and y times in $ t _2 $ yr.
Then, $ {x^{\frac{1}{t _1}}}={y^{\frac{1}{t _2}}} $
Given, $ t _1=3yr, $ $ t _2=?, $ $ x=3 $ and $ y=9 $
$ \Rightarrow $ $ {{(3)}^{\frac{1}{3}}}={{(9)}^{\frac{1}{t _2}}} $
$ \Rightarrow $ $ {{(3)}^{\frac{1}{3}}}={{(3)}^{\frac{2}{t _2}}} $
On comparing both sides, we get
$ \frac{2}{t _2}=\frac{1}{3} $
$ \therefore $ $ t _2=6yr $
$ \therefore $ The sum will become 9 times itself in 6 yr.
BETA
