MAT Exam 2025 Paper

Concept:Time and work are related by rates. If a pipe is faster, it takes less time. We use the relation $T_A = T_B - 36$ and $T_A = \frac{T_B}{3}$.Explanation:Let Pipe B take $t$ minutes alone.Since Pipe A is 3 times faster, Pipe A takes $\frac{t}{3}$ minutes alone.Given, Pipe A takes 36 minutes less than Pipe B:$$t - \frac{t}{3} = 36$$$$\Rightarrow \frac{2t}{3} = 36$$$$\Rightarrow t = 54 \text{ minutes}$$So, Pipe B alone takes 54 minutes.Pipe A alone takes $\frac{54}{3} = 18$ minutes.In 1 minute, Pipe A fills $\frac{1}{18}$ of the tank.In 1 minute, Pipe B fills $\frac{1}{54}$ of the tank.Combined rate:$$\frac{1}{18} + \frac{1}{54} = \frac{3+1}{54} = \frac{4}{54} = \frac{2}{27}$$Time taken when both are opened together:$$\text{Time} = \frac{1}{\frac{2}{27}} = \frac{27}{2} = 13.5 \text{ minutes}$$This equals $13\frac{1}{2}$ minutes.Answer:Option A: $13\frac{1}{2}$ min