MAT Exam 2023 Paper

Concept:Form a pair of linear equations from the given age conditions and solve for the present ages.Explanation:Let the present ages of mother and son be $M$ years and $S$ years respectively.One year ago, mother’s age was $M-1$ and son’s age was $S-1$.Given: $M-1 = 5(S-1)$So, $M = 5S - 4$ …(1)After 6 years, mother’s age will be $M+6$ and son’s age will be $S+6$.Given: $M+6 = 2(S+6) + 5$Substitute $M = 5S - 4$ into this equation:$(5S - 4) + 6 = 2(S + 6) + 5$$5S + 2 = 2S + 12 + 5$$5S + 2 = 2S + 17$$3S = 15$$S = 5$Now substitute $S = 5$ into equation (1):$M = 5(5) - 4 = 21$Therefore, the present ratio of mother’s age to son’s age is:$M : S = 21 : 5$Answer:$\boxed{21 : 5}$, which is option D.