MAT Exam 2021 Paper

Concept:Let the filling capacity be $x \,\mathrm{m^3/min}$. Then the emptying capacity is $(x+10) \,\mathrm{m^3/min}$. Use the difference in time taken to form an equation.Explanation:Time taken to fill the tank = $\frac{2400}{x}$ min.Time taken to empty the tank = $\frac{2400}{x+10}$ min.The pump takes 8 min less to empty the tank, so:$$\frac{2400}{x} - \frac{2400}{x+10} = 8$$$$\Rightarrow 2400\left[\frac{10}{x(x+10)}\right] = 8$$$$\Rightarrow x^2 + 10x - 3000 = 0$$$$\Rightarrow (x+60)(x-50) = 0$$Thus, $x = 50$ or $x = -60$. Since capacity cannot be negative, $x = 50$.Answer:The filling capacity of the pump is $50 \,\mathrm{m^3/min}$.Correct option: B. $50 \,\mathrm{m^3/min}$