MAT Exam 2020 Paper

Concept:This is a weighted average problem. The overall average salary is used to find the number of senior-level employees, then a percentage is applied to find total employees.Explanation:Let $x$ be the number of senior-level employees.Middle-level employees = 125 and their total salary = $125 \times 5500$.Senior-level employees total salary = $x \times 14000$.Using the weighted average formula:$$\frac{125 \times 5500 + x \times 14000}{125+x} = 8687.5$$Multiply both sides by $125+x$:$$687500 + 14000x = 8687.5(125+x)$$$$687500 + 14000x = 1085937.5 + 8687.5x$$$$5312.5x = 398437.5$$$$x = 75$$So middle + senior employees = $125 + 75 = 200$.Given: These 200 employees form $80\% = \frac{4}{5}$ of the total employees.Let total employees be $T$.$$\frac{4}{5}T = 200$$$$T = 200 \times \frac{5}{4} = 250$$Answer:The total number of employees in the company is $250$.Correct option: D.