# The father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age. The present ages, in years, of the son and the father are, respectively(A) 4 and 24(B) 5 and 30(C) 6 and 36(D) 3 and 24

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Given :

The father\'s age is six times his son\'s age. Four years hence, the age of the father will be four times his son\'s age.

To find :

We have to find the present ages of father and son.

Solution :

Let the present ages of the son and the father be $x$ and $y$ respectively.

This implies,

$y=6x$........(i)

Age of the son after 4 years $= x+4$

Age of the father after 4 years $= y+4$.

Therefore,

$y+4 = 4[x+4]$

$y+4 = 4x+16$

$y = 4x+16-4$

$y = 4x+12$.....(ii)

Substituting (i) in (ii), we get,

$6x=4x+12$

$6x-4x=12$

$2x=12$

$x=6$

$\Rightarrow y=6(6)=36$

The present age of the son is $6$ years and the present age of the father is $36$ years.

Updated on 10-Oct-2022 13:27:13