# The sum of the present age of a father and his son is 100 years. If the ratio between their ages 5 years ago was 2 : 1, what will be their age after 1

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The sum of the present age of a father and his son is 100 years. If the ratio between their ages 5 years ago was 2 : 1, what will be their age after 10 years?
1. 65 years, 55 years
2. 70 years, 50 years
3. 75 years, 45 years
4. 80 years, 40 years

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Correct Answer - Option 3 : 75 years, 45 years

Let the present age of the father be F and the present age of the son be S.
According to the question:
F + S = 100 years    ((i) equation)
Also,
$F - 5/ S - 5 = 2/1$
⇒ 2S - F = 5 years   ((ii) equation)
On solving these two equations, we get
S = 35 years
F = 65 years
The ages of the father and the son after 10 years would be 75 years and 45 years respectively.