MAT Exam 2024 Paper

Concept:If one pipe is 3 times faster, its time to fill alone is one-third of the slower pipe’s time.Explanation:Let the time taken by pipe T alone be $x$ minutes.Since pipe Z is 3 times faster, time taken by Z alone is $\frac{x}{3}$ minutes.Given, Z takes 32 minutes less than T:$$x - \frac{x}{3} = 32$$$$\Rightarrow \frac{2x}{3} = 32$$$$\Rightarrow x = 48 \text{ minutes}$$So, T alone takes 48 minutes.Z alone takes $\frac{48}{3} = 16$ minutes.Work done per minute by T = $\frac{1}{48}$.Work done per minute by Z = $\frac{1}{16}$.Combined work per minute:$$\frac{1}{48} + \frac{1}{16} = \frac{1+3}{48} = \frac{4}{48} = \frac{1}{12}$$Hence, together they fill the cistern in 12 minutes.Answer:Option D. 12 minutes