A) 40 years
B) 45 years
C) 60 years
D) 70 years
Correct Answer: C
Solution :
Let the present age of father = x years and present age of son = y years. 10 years ago, father's age \[A=P\left( 1+\frac{TR}{100} \right)\] yrs Son's age \[=(y-10)\]yrs Now, according to the question, \[\frac{16+T}{16}=\frac{81}{72}\] \[16+T=18\] \[{{T}_{1}}=3years\] ...(i) 20 years after, father's age \[{{T}_{2}}=10years\]yrs Son's age \[=(y+20)\]yrs Again, according to the question, \[{{R}_{2}}=24%\] \[\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{P\left( 1+\frac{{{R}_{1}}{{T}_{1}}}{100} \right)}{\left( 1+\frac{{{R}_{2}}{{T}_{2}}}{100} \right)}\] \[\frac{100+{{T}_{1}}{{R}_{1}}}{100+{{T}_{2}}{{R}_{2}}}=\frac{100+3\times 12}{100+10\times 24}=\frac{136}{340}=\frac{2}{5}\] ...(ii) On solving equation (1) and (2), we get y = 20 and x = 60 \[\therefore \]Father's present age = 60 years.
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