A) 8 yr
B) 12 yr
C) 16 yr
D) 24 yr
Correct Answer: B
Solution :
Let \[Rs.\,P\] be the given sum of money and \[{{T}_{1}}=4\,yr\] \[2P=P{{\left( 1+\frac{R}{100} \right)}^{4}}\] \[\Rightarrow \] \[2={{\left( 1+\frac{R}{100} \right)}^{4}}\] \[\Rightarrow \] \[{{2}^{1/4}}=\left( 1+\frac{R}{100} \right)\] ?(i) Let the sum become 8 times in Tyr. Then, \[8P=P{{\left( 1+\frac{R}{100} \right)}^{T}}\] \[\Rightarrow \] \[8={{\left( 1+\frac{R}{100} \right)}^{T}}\] \[\Rightarrow \] \[8={{({{2}^{\frac{1}{4}}})}^{T}}\] [from Eq. (i)] \[\Rightarrow \] \[8={{2}^{T/4}}\] \[\Rightarrow \] \[{{2}^{3}}={{2}^{T/4}}\] On comparing, \[3=\frac{T}{4}\] \[\Rightarrow \] \[T=12\,yr\]
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