Six years ago a father was seven times as old as his son. After six years he will be three times as old as his son. Determine their present ages.

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12, 48 years

14, 48 years

16, 48 years

18, 48 years

answer is A.

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Detailed Solution

Concept-
Let's use

x

as the son's current age in the son and father combination.
So, the son was roughly x years old six years ago.
Meanwhile, he was about

7 (x - 6)

years older than the father.
Thus, the father's current age is determined to be

7 (x - 6) + 6

years.
Likewise, the son's age after six years is x+6 years.
In a similar manner, the father will age to

7 (x - 6) + 6 + 6

years after six years.
As stated in the question, the father's age at this point will be three times that of the son. The father's age is therefore equal to the son's age when the numbers are entered into the equation:

7 (x - 6) + 6 + 6 = 3 (x + 6)

The value of the x variable is obtained by shifting the values of x and the variables in the LHS and RHS, respectively:

7 x - 42 + 12 = 3 x + 18

4 x - 30 = 18

4 x = 48

x = \frac{48}{4}

x = 12

Consequently, the common/unknown variable x has a value of 12.
Now that we've changed the value of x in the father and son's age equation, we can calculate their ages as follows: