Four years ago, the father's age was three times the age of his son. The total of the ages of the father and the son after four years will be 64 years. What is the father's age at present? Option 1) 32 years Option 2) 36 years Option 3) 44 years Option 4) Data inadequate Option 5) None of these
Question
Four years ago, the father's age was three times the age of his son. The total of the ages of the father and the son after four years will be 64 years. What is the father's age at present?
Option 1) 32 years
Option 2) 36 years
Option 3) 44 years
Option 4) Data inadequate
Option 5) None of these
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Answer
The correct option is None of these.
Let ( x ) represent the son's age 4 years ago. Consequently, the father's age 4 years ago would be ( 3x ) due to the given condition.
In 4 years, their ages will each increase by 8 years (4 years from the past to the present, and another 4 years into the future).
Hence, we can express their ages after 4 years as follows:
- Father's age after 4 years: ( (3x + 4) + 4 = 3x + 8 )
- Son's age after 4 years: ( x + 4 + 4 = x + 8 )
According to the problem, the sum of their ages at that time is 64 years: [ (3x + 8) + (x + 8) = 64 ]
Simplify the equation: [ 4x + 16 = 64 ]
Solving for ( x ): [ 4x = 64 - 16 ] [ 4x = 48 ] [ x = 12 ]
Thus, the son's age 4 years ago was 12 years. The father's age 4 years ago was: [ 3x = 3 \times 12 = 36 ]
Therefore, the father's present age is: [ 36 + 4 = 40 ]
Therefore, the present age of the father is 40 years, which does not match any of the given options. Hence, the correct option is None of these.
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