The sum of the ages of the father and his son is 100 years now 5 years ago their ages were in the ratio of 2:1. The ratio of the ages of the father and son after 10 years will be ____?
- 4:3
- 5:3
- 10:7
- None of these
Explanation
Current sum of ages = 100 years
5 years ago, their ages were in the ratio of 2:1. Let's call the father's age 5 years ago "2x" and the son's age 5 years ago "x".
We know that 5 years ago, their sum of ages was:
2x + x = 3x
Since the current sum of ages is 100, we can set up an equation:
(2x + 5) + (x + 5) = 100
Combine like terms:
3x + 10 = 100
Subtract 10 from both sides:
3x = 90
Divide by 3:
x = 30
So 5 years ago, the father's age was 2x = 60 and the son's age was x = 30.
Now, let's find their ages after 10 years:
Father's age = 60 + 5 + 10 = 75
Son's age = 30 + 5 + 10 = 45
The ratio of their ages after 10 years is:
75:45 = 5:3
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