MAT Exam 2020 Paper

Concept:Use the filling and emptying rates of the pipes to form an equation for the number of inlet pipes.Explanation:Let the number of inlet pipes be $x$.Total pipes are $6$, so the number of outlet pipes is $6-x$.Each inlet pipe fills the tank in $9$ hours, so its rate is $\frac{1}{9}$ tank per hour.Each outlet pipe empties the tank in $6$ hours, so its rate is $\frac{1}{6}$ tank per hour.When all pipes are opened together, the tank fills in $9$ hours, so the net rate is $\frac{1}{9}$ tank per hour.Thus, the equation is:$$\frac{x}{9}-\frac{6-x}{6}=\frac{1}{9}$$Multiply the whole equation by $18$:$$2x-3(6-x)=2$$Simplify:$$2x-18+3x=2 \Rightarrow 5x=20 \Rightarrow x=4$$Answer:The number of inlet pipes is $4$, i.e. option A.