Question : The sum of the present ages of a father and his son is 94 years. 8 years ago their respective ages were in the ratio of 2 : 1. After 10 years what will be the ratio of ages of father and son?
Option 1: 35 : 22
Option 2: 14 : 13
Option 3: 25 : 18
Option 4: 16 : 15
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Correct Answer: 35 : 22
Solution :
Let the present age of the father be $x$ and the present age of the son be $y$.
Given: $x + y = 94$.................(1)
8 yrs ago,
$\frac{x-8}{y-8}=\frac{2}{1}$
⇒ $x-8=2y-16$
⇒ $x-2y=-8$................(2)
Subtracting equation (2) from equation (1), we get:
$3y=102$
⇒ $y=34$
⇒ $x = 94-34=60$
$\therefore$ Son = 34 years and Father = 60 years
After 10 years,
The ratio of father and son ages = (60 + 10) : (34 + 10) = 70 : 44 = 35 : 22
Hence, the correct answer is 35 : 22.
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