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

Answer: Option C

Probability that A is telling the truth P(A)
= $$\frac{75}{100}$$ = $$\frac{3}{4}$$
Probability that B is telling the truth P(B)
= $$\frac{80}{100}$$ = $$\frac{4}{5}$$
Probability that A is lying P(A’)
= 1 - $$\frac{75}{100}$$ = $$\frac{25}{100}$$ = $$\frac{1}{4}$$
Probability that B is lying P(B’)
= 1 - $$\frac{80}{100}$$ = $$\frac{20}{100}$$ = $$\frac{1}{5}$$
Contradiction means either of
A telling truth and B lying
            Or
B telling truth and A lying
P(Contradiction)
= P(A) × P(B’) + P(A’) × P(B)
= $$\frac{3}{4}$$ × $$\frac{1}{5}$$ + $$\frac{1}{4}$$ × $$\frac{4}{5}$$
= $$\frac{7}{20}$$
$$\frac{7}{20}$$ is equal to 35 %.