30%

35%

40%

45%

B. 35%

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]

= $\left(\frac{3}{5}\times \frac{1}{5}\right)+\left(\frac{1}{4}\times \frac{4}{5}\right)=\frac{7}{20}$

= $\left(\frac{7}{20}\times 100\right)\%=35\%$

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{1}{2}$

$\frac{1}{8}$

$\frac{7}{19}$

$\frac{6}{19}$

$\frac{5}{19}$

$\frac{4}{19}$

30%

35%

40%

45%

$\frac{1}{13}$

$\frac{2}{13}$

$\frac{1}{26}$

$\frac{1}{52}$

$\frac{2}{121}$

$\frac{2}{221}$

$\frac{1}{221}$

$\frac{1}{13}$

$\frac{1}{3}$

$\frac{1}{9}$

$\frac{1}{12}$

$\frac{2}{9}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{5}$

$\frac{1}{6}$

1

2

$\frac{1}{2}$

0

$\frac{3}{4}$

$\frac{1}{4}$

$\frac{7}{4}$

$\frac{1}{2}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{3}{2}$

$\frac{3}{4}$

1

2

$\frac{1}{2}$

0

1

$\frac{2}{3}$

$\frac{1}{3}$

$\frac{4}{3}$

$\frac{4}{13}$

$\frac{1}{52}$

$\frac{1}{4}$

None of above

$\frac{52}{55}$

$\frac{3}{55}$

$\frac{41}{44}$

$\frac{3}{44}$

$\frac{2}{3}$

$\frac{8}{21}$

$\frac{3}{7}$

$\frac{9}{22}$