MAT Exam 2025 Paper

Concept:Use a weighted average to find the missing group’s mean by assuming the total number of students is 100.Explanation:Let the total number of students be 100.Let the average marks of the remaining students be $x$.Students who scored 79 marks = $13\%$ of 100 = 13.Students who scored 89 marks = $15\%$ of 100 = 15.Remaining students $=100-(13+15)=72$.Class average $=69.7$, so the total marks of the whole class is $69.7 \times 100 = 6970$.Total marks contributed by the two groups:$(13 \times 79)+(15 \times 89)=1027+1335=2362$.Now form the equation:$$69.7=\frac{1027+1335+72x}{100}$$Multiply both sides by 100:$$6970=2362+72x$$Subtract 2362 from both sides:$$72x=6970-2362=4608$$Divide by 72:$$x=\frac{4608}{72}=64$$Thus, the average marks of the remaining students is 64.Answer:64 marks (Option B).