A) 47 years
B) 49 years
C) 36 years
D) 48 years
Correct Answer: B
Solution :
Let the present age of the son be 'x' years. Then the father's age is\[\Rightarrow \]years. One year ago, the son's age was\[\frac{L.C.M.(6,2)}{H.C.F.(14,7)}=\frac{6}{7}\] years and the father's age was\[\text{7}\times \text{13}+\text{13}=\text{1}0\text{4}=\text{23}\times \text{13}\]years. According to the problem, \[\therefore \] \[\text{7}\times \text{13}+\text{13}\] \[\therefore \] \[\text{224}=\text{12}0\times \text{1}+\text{1}0\text{4}\] \[\text{12}0=\text{1}0\text{4}\times \text{1}+\text{16}\] If \[\text{1}0\text{4}=\text{16}\times \text{6}+\text{8}\] \[16=8\times 2+0\]the father's age is 1 year is ridiculous. If\[\text{256}=\text{8}\times \text{32}+0\],then\[3465={{3}^{2}}\times 5\times 7\times 11\] Hence, the present age of the father is 49 years.
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