A) \[1\frac{1}{3}\]
B) \[1\frac{1}{2}\]
C) \[2\frac{1}{3}\]
D) \[2\frac{1}{2}\]
Correct Answer: B
Solution :
Let the required time be t yr. Then, P = Rs. 800, R = 5% per semi ? annual, time = 2r half- years \[\therefore \]Amount\[\left[ 800\times {{\left( 1+\frac{5}{100} \right)}^{2t}} \right]\] \[\left[ 800\times {{\left( \frac{21}{20} \right)}^{2t}} \right]\] \[\therefore \,\]\[800\times {{\left( \frac{21}{20} \right)}^{2t}}=\frac{92610}{100}\] \[\Rightarrow \,\]\[{{\left( \frac{21}{20} \right)}^{2t}}=\frac{92610}{800\times 100}=\frac{9261}{8000}={{\left( \frac{21}{20} \right)}^{3}}\] \[\Rightarrow \,\] \[2\text{t}=3\] \[\Rightarrow \,\] \[t=\frac{3}{2}yr=1\frac{1}{2}yr\]
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