Explanation:

Let's break down the information:

- The age of Q is P's age plus 3 years: Q = P + 3

- R's age is twice that of P: R = 2P

- Q's age is twice that of S: Q = 2S

- The difference between R and S's ages is 30 years: R - S = 30

Now, let's express everything in terms of P:

- R = 2P

- Q = P + 3

- S = Q / 2 = (P + 3) / 2

- The equation R - S = 30 gives us:

$$ 2P - \frac{(P + 3)}{2} = 30 $$

Solve for P:

- Multiply everything by 2 to eliminate the fraction:

$$ 4P - (P + 3) = 60 $$

- Simplify:

$$ 4P - P - 3 = 60 $$

$$ 3P = 63 $$

$$ P = 21 $$

Now, find Q:

- Q = P + 3 = 21 + 3 = 24

Sum of the ages of P and Q is:

- P + Q = 21 + 24 = 45 years

So, the correct option is:

Option 4: 45 years