MAT Exam 2021 Paper

Concept:Add the fractions of the tank filled by each pipe in one hour to account for the alternating one-hour periods.Explanation:Pipe $A$ fills $\frac{1}{30}$ of the tank in 1 hour.Pipe $B$ fills $\frac{1}{45}$ of the tank in 1 hour.When both pipes work alternately for 1 hour each, the part filled in a 2-hour cycle is$\frac{1}{30}+\frac{1}{45}=\frac{3+2}{90}=\frac{1}{18}$.So after one 2-hour cycle, $\frac{1}{18}$ of the tank is filled.Therefore, 18 such cycles will fill the tank completely.Each cycle takes 2 hours, so the total time is$18 \times 2 = 36\ \text{hours}$.Answer:The tank will be filled in $\boxed{36}$ hours, i.e. option A.