Let the probability that A and B speak truth be P(A) and P(B) respectively.
Therefore, P (A) = $\frac{60}{100}$ = $\frac{3}{5}$ and P (B) = $\frac{90}{100}$ = $\frac{9}{10}$
A and B can contradict in stating a fact when one is speaking the truth and other is not speaking the truth.
Case 1: A is speaking the truth and B is not speaking the truth.
Required probability = P (A) × 1 - P (B) = $\frac{3}{5}\times \left(1-\frac{9}{10}\right)$ = $\frac{3}{50}$
Case 2: A is not speaking the truth and B is speaking the truth.
Required probability = 1 - P (A) × P (B) = $\left(1-\frac{3}{5}\right)$ × $\frac{9}{10}$ = $\frac{9}{25}$
∴ Percentage of cases in which they are likely to contradict in stating the same fact = $\left(\frac{3}{50}+\frac{9}{25}\right)$ × 100% = $\left(\frac{3+18}{50}\right)$ × 100% = 42%
From case 1, it is clear that it is not necessary that the statement of B will carry more weight as he speaks truth in more number of cases than A.