A speaks the truth in 75% cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?

Probability of A speaks truth $$=P\left(A\right)=0.75$$
Probability of A speaks lie $$=P\left(\overline{A}\right)=0.25$$
Probability of B speaks truth $$=P\left(B\right)=0.8$$
Probability of B speaks lie $$=P\left(\overline{B}\right)=0.2$$

A and B will contradict each other when A is speaking the truth and B is speaking lie or A is speaking lie and B is speaking the truth.

$$P(C)=P\left(A\right)P\left(\overline{B}\right)+P\left(B\right)P\left(\overline{A}\right)$$

$$P(C)=0.75\times0.2+0.8\times0.25$$

$$P(C)=0.15+0.2=0.35$$

Thus, the chances of A and B contradicting each other is 35%.