MAT Exam 2024 Paper

Concept:Agreement occurs when both persons either tell the truth or both lie.Explanation:Odds of P agreeing with truth are $3:2$.So, probability that P tells the truth is $\frac{3}{3+2}=\frac{3}{5}$.Probability that P lies is $1-\frac{3}{5}=\frac{2}{5}$.Odds of Q agreeing with truth are $5:3$.So, probability that Q tells the truth is $\frac{5}{5+3}=\frac{5}{8}$.Probability that Q lies is $1-\frac{5}{8}=\frac{3}{8}$.They agree with each other if both tell the truth or both lie.$P(\text{agree}) = P(\text{both truth}) + P(\text{both lie})$$= \frac{3}{5} \times \frac{5}{8} + \frac{2}{5} \times \frac{3}{8}$$= \frac{15}{40} + \frac{6}{40} = \frac{21}{40}$Percentage $= \frac{21}{40} \times 100 = 52.5\%$.Answer:$52.5\%$; therefore, the correct option is D. None of these.