Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?
Given :
Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age.
To do :
We have to find the present ages of Salim and his daughter.
Solution :
Let the ages of Salim and his daughter be $x$ and $y$ respectively.
This implies,
Age of Salim 2 years ago $= x-2$ years.
Age of the daughter 2 years ago $= y-2$ years.
Age of Salim after 6 years $= x+6$ years.
Age of the daughter after 6 years $= y+6$ years.
According to the question,
$x+6=2(y+6)+4$
$x+6=2y+12+4$
$x=2y+16-6$
$x=2y+10$.....(i)
$x-2=3(y-2)$
$x-2=3y-6$
$3y=(2y+10)+6-2$ (From (i))
$3y=2y+10+4$
$3y-2y=14$
$y=14$
$\Rightarrow x=2(14)+10=28+10=38$
The present ages of Salim and his daughter are 38 years and 14 years respectively.
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