Age Problem Setup

Let Narendra's present age be represented by $N$ and his mother's present age by $M$.

Formulating Age Equations

From the first statement, "Narendra's mother is four times as old as Narendra", we get the equation:

$ M = 4N \quad (1) $

From the second statement, "Four years ago, his mother was six times as old as Narendra was", we consider their ages four years ago:

• Narendra's age 4 years ago: $N - 4$
• Mother's age 4 years ago: $M - 4$

This gives us the second equation:

$ M - 4 = 6(N - 4) \quad (2) $

Solving the Equations

Substitute the value of $M$ from equation (1) into equation (2):

$ 4N - 4 = 6(N - 4) $

Distribute the 6 on the right side:

$ 4N - 4 = 6N - 24 $

Rearrange the terms to solve for $N$:

$ 24 - 4 = 6N - 4N $

$ 20 = 2N $

$ N = \frac{20}{2} $

$ N = 10 $

Now, find the mother's age $M$ using equation (1):

$ M = 4N = 4 \times 10 $

$ M = 40 $

Verifying the Solution

Check if the ages satisfy the conditions:

• Present ages: Narendra is 10, Mother is 40. Is $40 = 4 \times 10$? Yes.
• Ages 4 years ago: Narendra was $10 - 4 = 6$, Mother was $40 - 4 = 36$. Is $36 = 6 \times 6$? Yes.

Both conditions are met.

Final Ages Answer

Narendra's present age is 10 years and his mother's present age is 40 years.