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?

Solution(By Examveda Team)

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 %.