Explanation:

- Let's denote the three numbers as \(a\), \(b\), and \(c\).

- The conditions are:

- \(a + b + c = 50\),

- \(abc = 3750\),

- \(\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{31}{150}\).

- Using the identity \(\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{ab + bc + ca}{abc}\), we have:

- \( \frac{ab + bc + ca}{3750} = \frac{31}{150} \implies ab + bc + ca = 775 \).

- The sum of squares can be calculated using \((a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)\).

- Substituting the values:

- \(50^2 = a^2 + b^2 + c^2 + 2(775)\),

- \(2500 = a^2 + b^2 + c^2 + 1550\),

- \(a^2 + b^2 + c^2 = 950\).

- Thus, the correct option is Option:3, 950.