MAT Exam 2022 Paper

Concept:Use total work as the LCM of the individual filling times, then convert each pipe’s time into a rate.Explanation:From the graph: E takes 12 minutes, F takes 18 minutes, and R takes 24 minutes to fill the tank alone.Let total capacity of the tank be $\mathrm{LCM}(12,18,24)=72$ units.Rates: E $=72/12=6$ units/min, F $=72/18=4$ units/min, R $=72/24=3$ units/min.So, E + F + R together fill $6+4+3=13$ units in 1 minute.R is closed 12 minutes before the tank is filled, meaning R works for $(t-12)$ minutes while E and F work for the full $t$ minutes.Total work equation: $13t - 3 \times 12 = 72$.$13t - 36 = 72 \Rightarrow 13t = 108 \Rightarrow t = \frac{108}{13} = 8\frac{4}{13}$ minutes.Answer:The tank is full in $8\frac{4}{13}$ minutes, which is option B.