A is x% more than B and is x% of sum of A and B. What is the value of x?

Let x% be the given percentage and write p = x/100 (so p is x in decimal form).

1. A is x% more than B, so A = B(1 + p).

2. Also A is x% of (A + B), so A = p(A + B).

3. From the first equation, B = A/(1 + p). From the second, rearrange to get B = A(1 - p)/p.

4. Equate the two expressions for B: 1/(1 + p) = (1 - p)/p. Multiply both sides to obtain p = 1 - p^2.

5. Bring all terms to one side: p^2 + p - 1 = 0. Solve this quadratic: p = (-1 ± sqrt(5))/2.

6. Only the positive root between 0 and 1 is valid: p = (-1 + sqrt(5))/2 ≈ 0.618.

Therefore x = 100·p ≈ 61.8%.

Answer: x ≈ 62%