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

Correct Answer : B.

Let A = Event that A speaks the truth
B = Event that B speaks the truth
Then P(A) =$\frac{75}{100} = \frac{3}{4}$
P(B) =$\frac{ 80}{100}= \frac{4}{5}$
P(A-lie) = $1-\frac{3}{4} = \frac{1}{4}$
P(B-lie) = $1-\frac{4}{5}= \frac{1}{5}$
Now, A and B contradict each other = [A lies and B true] or [B true and B lies]
= P(A).P(B-lie) + P(A-lie).P(B)
[Please note that we are adding at the place of OR]
= $\left(\frac{3}{5}\times \frac{1}{5}\right)+\left(\frac{1}{4}\times \frac{4}{5}\right)= \frac{7}{20}$
= $\left(\frac{7}{20} \times 100\right)\% = 35\%$