A Mathematical Puzzler: Solving the Age Mystery of a Father and His Son

Mathematics is a powerful tool for understanding and solving real-life problems, even some as simple as determining the current ages of family members. This article explores a classic problem involving the ages of a father and his son, breaking it down into a detailed solution using algebraic equations.

Introduction

The problem presented here is a classic example of a linear equation with two variables. We can solve it to find both the father's and the son's current ages. Let's delve into the solution step-by-step.

Problem Statement

Rohit was 4 times as old as his son 8 years ago. After 8 years, Rohit will be twice as old as his son. What are their current ages?

Let's denote Rohit's current age as (R) and his son's current age as (S).

Setting Up the Equations

We have the following key pieces of information:

1. 8 years ago, Rohit was 4 times as old as his son:

[R - 8 4(S - 8)]

2. 8 years from now, Rohit will be twice as old as his son:

[R 8 2(S 8)]

Simplifying the Equations

First, let's simplify the first equation:

[R - 8 4(S - 8)] [R - 8 4S - 32] [R 4S - 24 quad text{(Equation 1)}]

Next, let's simplify the second equation:

[R 8 2(S 8)] [R 8 2S 16] [R 2S 8 quad text{(Equation 2)}]

Solving the Equations

Now we can set the two equations for (R) equal to each other:

[4S - 24 2S 8] Solving for (S):
[4S - 2S 8 24] [2S 32] [S boxed{16 text{ years} quad (The son's current age)}]

Now substitute (S 16) back into either equation to find (R):

[R 4S - 24] [R 4 cdot 16 - 24] [R 64 - 24] [R boxed{40 text{ years} quad (The father's current age)}]

Thus, the father is 40 years old, and his son is 16 years old.

Verification

To verify the solution, let's substitute the values back into the original conditions:

1. 8 years ago, Rohit was 4 times as old as his son:

[40 - 8 4 cdot (16 - 8)] [32 4 cdot 8] [32 32]

2. 8 years from now, Rohit will be twice as old as his son:

[40 8 2 cdot (16 8)] [48 2 cdot 24] [48 48]

Both conditions are satisfied.

Conclusion

The ages of the father and son are 40 and 16, respectively. This solution demonstrates the power of algebraic equations in solving real-world problems, providing a clear and concise method for determining the ages of family members based on given conditions.