The sum of the present ages of father and his son is 60 years. 6 years ago, father age was five times the age of the son. After six years son's age will bea)20 yearsb)14 yearsc)12 yearsd)18 yearsCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Sum of present ages of father and son:

Let the present age of the father be F and the present age of the son be S.

According to the given information, the sum of their ages is 60. Therefore, we can write the equation:

F + S = 60

Age relationship six years ago:

Six years ago, the father's age would have been F - 6 and the son's age would have been S - 6.

According to the given information, the father's age six years ago was five times the age of the son. Therefore, we can write the equation:

F - 6 = 5(S - 6)

Solving the equations:

We can solve the above equations simultaneously to find the values of F and S.

From the first equation, we can express F in terms of S:

F = 60 - S

Substituting this value in the second equation:

60 - S - 6 = 5(S - 6)

Simplifying the equation:

54 - S = 5S - 30

Combining like terms:

6S = 84

Dividing both sides by 6:

S = 14

Substituting the value of S in the first equation:

F + 14 = 60

F = 60 - 14

F = 46

Therefore, the present age of the father is 46 years and the present age of the son is 14 years.

Age after six years:

After six years, the father's age will be F + 6 and the son's age will be S + 6.

Substituting the values:

Father's age after six years = 46 + 6 = 52

Son's age after six years = 14 + 6 = 20

Therefore, after six years, the son's age will be 20 years, which corresponds to option A.

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