The sum of the present ages of a father and his son is 126 years. 8 years ago their respective ages were in the ratio of 7 : 4. After 7 years what will be the ratio of ages of father and son?

The sum of the present ages of a father and his son is 126 years. 8 years ago their respective ages were in the ratio of 7 : 4. After 7 years what will be the ratio of ages of father and son?
1). 23 : 19 
2). 17 : 11
3). 27 : 20
4). 34 : 23

8 year ago the ratio of age of father and his son was $7 : 4$

Let the father and son age be $7x$ and $4x$ respectively

Present age of father and son is $(7x + 8)$ and $(4x + 8)$ respectively

According to question,

$(7x + 8) + (4x + 8) = 126$

$11x + 16 = 126$

$x = 10$

Present age of father $= (7x + 8) = 78$ years and present age of son $= (4x + 8) = 48$ years

After $7$ years, father $= 78 + 7 = 85$ years and son $= 48 + 7 = 55$ years

After $7$ years the ratio of ages of father and son $= 85 : 55 = 17 : 11$

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