10 years ago. a father's age was $$3\frac{1}{2}$$ times that of his son, and 10 years from now, the fathers age will be $$2\frac{1}{4}$$ times that of the son. What will be the sum of the ages of the father and the son at present?
Let the present age of the son is x years and father's age is y years.
10 Year before, the age of the son was =x-10 and age of father =y-10
As per the condition given in the question,
$$y-10=\dfrac{7(x-10)}{2}$$
$$\Rightarrow 2y-20=7x-70$$
$$\Rightarrow 7x-2y=50------(i)$$
Now, The age of son after 10 year, will be $$x+10$$ and father's age $$=y+10$$
as per the given condition in the question,
$$\Rightarrow y+10=\dfrac{9(x+10)}{4}$$
$$\Rightarrow 4y+40=9x+90$$
$$\Rightarrow 9x-4y=-50 ------(ii)$$
From the equation (i) and (ii),
$$x=30years$$ and $$y=80years$$
Hence the sum of the age=$$80+30=110$$years
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