Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-39

A sum of money at compound interest amounts to thrice itself in 3 yr. In how many years will it be 9 times itself?                                                                                                                       [ISSC (CGL) 2012]

A) 9 yr

B) 27 yr

C) 6 yr

D) 3 yr

Correct Answer: C

Solution :

Let \[A=Rs.\,\,3x,\]\[P=Rs.\,\,x\]

\[\because \] \[A=P{{\left( 1+\frac{r}{100} \right)}^{t}}\]

Then, \[3x=x{{\left( 1+\frac{r}{100} \right)}^{3}}\]\[\Rightarrow \]\[3=1{{\left( 1+\frac{r}{100} \right)}^{3}}\]

On squaring both sides, we get

\[9=1{{\left( 1+\frac{r}{100} \right)}^{6}}\]

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, \[{{t}_{1}}=3\,\,yr,\]\[{{t}_{2}}=?,\]\[x=3\]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.