MAT Exam 2024 Paper

Concept:Use total weight equations formed after each new student is added to find the original average.Explanation:Let the original average weight be $x$ kg and the original number of students be $n$.When one student weighing $50$ kg is added, the new average becomes $x+1$ kg.Total weight equation: $\frac{nx+50}{n+1} = x+1$.Simplifying gives $50 - x = n + 1$.Now, when one more student weighing $50$ kg is added, the new average becomes $x + 1.5$ kg.Total weight equation: $\frac{nx+100}{n+2} = x + 1.5$.Simplifying gives $100 - 2x = 1.5(n+2)$.From the first equation, we get $n = 49 - x$.Substitute this value into the second equation: $100 - 2x = 1.5(49 - x + 2)$.So, $100 - 2x = 1.5(51 - x)$.This simplifies to $100 - 2x = 76.5 - 1.5x$.Therefore, $0.5x = 23.5$, giving $x = 47$.Answer:The original average weight of the class is $47$ kg, which is option D.