Gaurav's Age

Gaurav's current age is unknown, so let's represent his age as 'x' years.

Mother's Age

According to the problem, Gaurav's mother is 28 years older than him. So, we can represent her age as 'x + 28' years.

Five Years Ago

To solve the problem, let's consider the situation five years ago. We will subtract 5 years from both Gaurav's and his mother's age.

Gaurav's age five years ago: x - 5 years.
Mother's age five years ago: (x + 28) - 5 years.

Ratio of Ages

According to the problem, Gaurav's mother was 5 times as old as Gaurav five years ago. So, we can set up the following equation:

(x + 28) - 5 = 5(x - 5)

Solving the Equation

Let's solve the equation to find Gaurav's age.

x + 28 - 5 = 5x - 25

Combine like terms:

x + 23 = 5x - 25

Subtract 'x' from both sides:

23 = 4x - 25

Add '25' to both sides:

48 = 4x

Divide both sides by '4':

x = 12

Present Ages

Now that we know Gaurav's age (x = 12), we can find the present ages of Gaurav and his mother.

Gaurav's present age: x = 12 years
Mother's present age: x + 28 = 12 + 28 = 40 years

Summary

Based on the given information, Gaurav's mother is currently 40 years old, and Gaurav is currently 12 years old. Their ages satisfy the condition that Gaurav's mother is 28 years older than him, and five years ago, she was 5 times as old as Gaurav.