Age Riddle and Its Mathematical Solution

Many intriguing age riddles challenge our mathematical skills and logical reasoning. One such riddle asks: If the present age of a man is four times that of his son, and after two years, their combined ages will be 44, what is the present age of his son? This riddle offers a fun and engaging way to explore algebraic concepts and solve real-world problems using mathematical tools.

Setting Up the Problem

To solve this riddle, we start by defining the variables:

Son's age now: s

Man's age now: 4s

Given that the man's age is four times the son's age, we can express the man's current age as a multiple of the son's age.

Future Ages and the Given Information

In two years, the son's age will be increased by two years, so:

Son’s age to come: s 2

Man’s age to come: 4s 2

The problem states that in two years, their combined ages will be 44:

(s 2) (4s 2) 44

Solving the Equation

Combining like terms, we get:

5s 4 44

5s 44 - 4

5s 40

s 40 / 5

s 8

Thus, the son's present age is s 8 years.

Verification and Additional Solutions

Let's verify the solution:

The son's current age is 8 years.

The man's current age is 4 * 8 32 years.

In two years, their combined ages will be:

(8 2) (32 2) 10 34 44

This confirms our solution is correct.

Alternative Solutions

Let's explore an alternative approach:

Denote the father's current age as F and the son's current age as S 44 - F.

In two years, the father's age will be F 2 and the son's age will be S 2 46 - F.

Given that in two years, the father’s age will be twice the son’s age:

F 2 2(S 2)

F 2 2(46 - F 2)

F 2 2(48 - F)

F 2 96 - 2F

3F 94

F 31.33

This approach does not yield integer ages and seems more complex, thus confirming the simpler solution.

Conclusion

The correct answer to the age riddle is: the son's present age is 8 years, and the father's present age is 32 years. These ages satisfy the conditions of the problem, as their combined ages will be 44 in two years.

This riddle demonstrates the power of algebra in solving real-world problems, and it can be a fun challenge for both students and adults to solve such puzzles.