10 years ago, a man’s age was 5 times of his son’s age. 2 years hence, twice his age will be equal to 4 times the age of his son. What is the present age (in years) of the son?
Correct Answer :
14
Solution :
The correct option is 14.
Let the present age of the son be s years and the present age of the father (man) be f years.
Step 1: Formulate the equation for 10 years ago.
10 years ago:
Son's age = s - 10
Father's age = f - 10
According to the given condition, 10 years ago, the man's age was 5 times his son's age:
--- (Equation 1)
Step 2: Formulate the equation for 2 years hence (in the future).
2 years from now:
Son's age = s + 2
Father's age = f + 2
According to the given condition, twice the man's age will be equal to 4 times the age of his son:
Divide both sides by 2:
--- (Equation 2)
Step 3: Solve for the present age of the son (s).
Equating Equation 1 and Equation 2:
Thus, the present age of the son is 14 years.
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