The probability that A speaks truth is 35 and that of B speaking truth is 47 . What is the probability that they agree in stating the same fact?

Answer: Option A

If both agree stating the same fact, either both of them speak truth of both speak false.
∴ Probability
$$\begin{array}{rl}& =\frac{3}{5}\times \frac{4}{7}+\frac{2}{5}\times \frac{3}{7}\\ & =\frac{12}{35}+\frac{6}{35}\\ & =\frac{18}{35}\end{array}$$