Question

The present age of a father is 10years more than twice the present age of his son.in how many years time will the age of the father be twice the age of the son

Answer 1

Let's denote the present age of the son as \( S \) years. According to the information given, the present age of the father is \( 2S + 10 \) years.

We want to find out in how many years, say \( x \), the age of the father will be twice the age of the son. In \( x \) years, the father's age will be \( 2S + 10 + x \) and the son's age will be \( S + x \).

We set up the equation based on the condition that the father's age will be twice the son's age:

\[
2S + 10 + x = 2(S + x)
\]

Now, expanding the right-hand side of the equation gives:

\[
2S + 10 + x = 2S + 2x
\]

Next, we can simplify this equation by subtracting \( 2S \) from both sides:

\[
10 + x = 2x
\]

Now, rearranging the equation gives:

\[
10 = 2x - x
\]
\[
10 = x
\]

Thus, in \( 10 \) years, the father's age will be twice the son's age.