Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be."

Consider Aftab's age asxand his daughter's age asy.Then , seven years ago,Aftab's age=x−7His daughter's age=y−7According to the question,x−7=7(y−7)x−7=7y−49x−7y=−49+7x−7y=−42…(i)After three years,Aftab's age=x+3His daughter's age=y+3According to the question,x+3=3(y+3)x+3=3y+9x−3y=9−3x−3y=6…(ii)Representing equation(i)and(ii)geometrically, we plot these equations by finding points on the lines representing these two equationsx−7y=−42⟹x=7y−42x=7y−42423549y121113x−3y=6⟹x=3y+6x=3y+6423648y121014From the graph we can see that two lines will intersect at a point.x−7y=−42x−3y=6On subtracting the two equations, we get4y=48ory=12Substituting value ofyin (2),x−36=6∴x=42