Aditya's father's present age is five times his present age. Two year from now, Aditya's age will be one fourth of his father's age at that time. Find both Aditya's and his father's present age.

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Solution

Let Aditya's Age is $x$
and his Father's Age be $y$

Hence, at present $y = 5 x . . . . . . . . . . . . (1)$

and 2 Year from now
$x + 2 = \frac{y + 2}{4} \Rightarrow 4 x + 8 = y + 2 \Rightarrow 4 x - y = - 6 . . . . . . . . . . . . . . . (2)$

From (1) and (2)
$4 x - 5 x = - 6 \Rightarrow x = 6$

and $y = 5 x = 5 * 6 = 30$

Hence, Aditya's present age = 6
His father's present age = 30

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Aditya's father's present age is five times his present age. Two year from now, Aditya's age will be one fourth of his father's age at that time. Find both Aditya's and his father's present age.

Let Aditya's Age is xand his Father's Age be yHence, at present y=5x............(1)and 2 Year from nowx+2=y+24⇒4x+8=y+2⇒4x−y=−6...............(2)From (1) and (2)4x−5x=−6⇒x=6and y=5x=5∗6=30Hence, Aditya's present age = 6His father's present age = 30