The present age of P is two times of Q and the present age of R is eight years more than that of Q. After three years, the average age of P, Q and R will be 11 years. Find the age of R two years hence (in years).

To find the age of R two years hence, let's define the present ages of P, Q, and R in terms of \(Q\)'s age. Let \(Q\)'s present age be \(q\).

Given:
1. \(P\)'s present age is \(2q\).
2. \(R\)'s present age is \(q + 8\).

After three years, the ages will be:
- \(P\) will be \(2q + 3\).
- \(Q\) will be \(q + 3\).
- \(R\) will be \(q + 8 + 3 = q + 11\).

We know that the average age of \(P\), \(Q\), and \(R\) after three years is 11 years:
\[
\frac{(2q + 3) + (q + 3) + (q + 11)}{3} = 11
\]

Let's solve this equation:

\[
\frac{(2q + 3) + (q + 3) + (q + 11)}{3} = 11
\]

Combine the terms in the numerator:

\[
\frac{2q + 3 + q + 3 + q + 11}{3} = 11
\]

Simplify the numerator:

\[
\frac{4q + 17}{3} = 11
\]

Multiply both sides by 3 to eliminate the denominator:

\[
4q + 17 = 33
\]

Subtract 17 from both sides:

\[
4q = 16
\]

Divide both sides by 4:

\[
q = 4
\]

Now, we know \(Q\)'s present age is 4 years. Let's find \(R\)'s present age:

\[
R = q + 8 = 4 + 8 = 12
\]

To find the age of \(R\) two years hence:

\[
R + 2 = 12 + 2 = 14
\]

Therefore, the age of \(R\) two years hence is \(14\) years.

Would you like more details or have any questions?

Here are some questions you can ask:
1. How do you find the average age given the ages of individuals?
2. What are the steps to solve an equation with multiple variables?
3. How do you simplify algebraic expressions?
4. What is the process to solve word problems involving ages?
5. Can you explain the concept of forming equations from word problems?

**Tip:** When dealing with word problems, clearly define each variable and translate the problem into mathematical equations step-by-step.

Learn how to solve a problem involving ages with a step-by-step solution. Given the relationships between ages of P, Q, and R, find the age of R two years hence. Suitable for students in Grades 7-9.

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