Solving the Age Problem: Aman's Age and His Son's Age Relationship

Today, we explore an interesting age problem from algebra. The problem presents a scenario involving Aman, his son, and their age relationship. Through a series of logical equations and step-by-step solutions, we will uncover their present ages and validate the given conditions.

Introduction to the Problem

Aman's age is three times his son's age. Ten years ago, Aman's age was five times his son's age. Let's unravel these conditions to find their present ages.

Setting Up the Equations

We denote the present age of the son as s and Aman's present age as m. According to the problem:

m 3s Twelve years ago, Aman's age was (m - 12) and his son’s age was (s - 12) At that time, Aman's age was five times his son's age:

m - 12 27s - 12

Solving the Equations

The given equations are:

m 3s m - 12 27s - 12

Substituting the first equation into the second:

m - 12 27s - 12

3s - 12 27s - 12

Let's simplify and solve for s:

3s - 12 27s - 12

3s - 27s -324

-24s -312

s 312 / 24

s 13

The son's present age is 13 years. Now, let's find Aman's age:

m 3s

m 3 * 13

m 39

Aman's present age is 39 years.

Validation of the Solution

To verify our solution, let's look at the situation twelve years ago:

Son's age twelve years ago: s - 12 13 - 12 1 year Aman's age twelve years ago: m - 12 39 - 12 27 years At that time, Aman's age was 27, and his son's age was 1, confirming the condition:

27 times 1 equals 27.

Conclusion

Through a series of algebraic equations, we have successfully found the present ages of Aman and his son. The son is currently 13 years old, and Aman is 39 years old. This solution satisfies the given conditions, making the problem not just an interesting exercise but a great example of applying algebraic reasoning.