A speaks truth in 60% cases B speaks truth in 70% cases. The probability that they will way say the same thing while describing a single event, is-

Answer: Option A

Let $$E_1$$ = event that A speaks the truth
And $$E_2$$ = event that B speaks the truth
Then,
$$\begin{array}{rl}& P\left(E_1\right)=\frac{60}{100}=\frac{3}{5},\\ & P\left(E_2\right)=\frac{70}{100}=\frac{7}{10},\\ & P\left({\bar{E}}_1\right)=\left(1-\frac{3}{5}\right)=\frac{2}{5},\\ & P\left({\bar{E}}_2\right)=\left(1-\frac{7}{10}\right)=\frac{3}{10}\end{array}$$
P (A and B say the same thing) = P [(A speaks the truth and B speaks the truth) or (A tells a lie and B tells a lie)]
$$=$$ P [$$\left(E_1\cap E_2\right)$$   or   $$({\overline{E}}_1\cap {\overline{E}}_2)]$$
$$=$$ P $$\left(E_1\cap E_2\right)$$   + $$({\overline{E}}_1\cap {\overline{E}}_2)$$
$$=$$ P ($$E_1$$). P ($$E_2$$) + P ($${\overline{E}}_1$$) . P ($${\overline{E}}_2$$)
$$\begin{array}{rl}& =\left(\frac{3}{5}\times \frac{7}{10}\right)+\left(\frac{2}{5}\times \frac{3}{10}\right)\\ & =\frac{27}{50}\\ & =0.54\end{array}$$