MAT Exam 2023 Paper

Concept:Use the formula for combined average: total sum of ages divided by total number of students.Explanation:Let the number of boys be $x$.Number of girls $= 20$.Average age of boys $= 20$ years, so total age of boys $= 20x$.Average age of girls $= 15$ years, so total age of girls $= 15 \times 20 = 300$.Combined average age of the class is $18$ years.Write the equation:$$\frac{20x + 300}{x + 20} = 18$$Multiply both sides by $x + 20$:$$20x + 300 = 18x + 360$$Simplify:$$20x - 18x = 360 - 300$$$$2x = 60$$$$x = 30$$So, the number of boys in the class is $30$.Answer:Option C, $30$