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, we have \[2P=P{{\left( 1+\frac{R}{100} \right)}^{4}}\] Or \[2={{\left( 1+\frac{R}{100} \right)}^{4}}\] Or \[{{2}^{\frac{1}{4}}}=\left( 1+\frac{R}{100} \right)\] ? (i) Let the sum become 8 times in T years, then \[8P=P{{\left( 1+\frac{R}{100} \right)}^{T}}\] Or \[8={{\left( 1+\frac{R}{100} \right)}^{T}}\] \[8={{\left( {{2}^{\frac{1}{4}}} \right)}^{T}}\] Or \[8={{2}^{\frac{T}{4}}}\] Or \[{{2}^{3}}={{2}^{\frac{T}{4}}}\] Or \[T=4\times 3=12\,\,yr.\]
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