A) 18 years 6 months
B) 16 years 8 months
C) 15 years 8 months
D) 16 years 10 months
Correct Answer: B
Solution :
Let the sum be Rs. x. Then amount \[Rs.\,=\,2x\] \[\therefore \] \[S.I=Rs.\,\,(2x-x)=Rs.\,x\] Time \[=8\frac{4}{12}\] years \[=\frac{25}{3}\]years Thus, \[P=Rs.\,x,\,\,S.I=Rs.x\] and \[T=\frac{25}{3}\] years \[\therefore \] Rate \[=\frac{100\times S.I}{P\times T}\] \[=\left( \frac{100\times x}{x}\times \frac{3}{25} \right)%p.a=12%\,p.a.\] Again, Sum \[=Rs.\,\,x,\] amount \[=Rs.\,\,3x,\] and rate = 12% p.a. Then, S.I \[=Rs.\,\,(3x-x)=Rs.\,2x\] \[\therefore \] \[P=Rs.\,x,\,\,S.I.=Rs.\,2x\] and R = 12% p.a. Time \[=\frac{100\times S.I}{P\times R}\] \[=\left( \frac{100\times 2x}{x\times 12} \right)\]years \[=\frac{50}{3}\] years = 16 years 8 months
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