MAT Exam 2021 Paper

Concept:Use the given rate ratio to find the actual filling/emptying rates, then calculate the net fill in each hour.Explanation:Let the rates of pipes A, B and C be $2x$, $3x$ and $4x$ respectively.A and B together fill the tank in 3 hours, so their combined rate is $\frac{1}{3}$ tank per hour.Therefore, $2x + 3x = \frac{1}{3}$, giving $x = \frac{1}{15}$.So, A's rate $= \frac{2}{15}$, B's rate $= \frac{3}{15} = \frac{1}{5}$, and C's rate $= \frac{4}{15}$ tank per hour.Hour 1: A empties, while B and C fill.Net fill $= -\frac{2}{15} + \frac{3}{15} + \frac{4}{15} = \frac{5}{15} = \frac{1}{3}$.Hour 2: B empties, while A and C fill.Net fill $= \frac{2}{15} - \frac{3}{15} + \frac{4}{15} = \frac{3}{15} = \frac{1}{5}$.Hour 3: C empties, while A and B fill.Net fill $= \frac{2}{15} + \frac{3}{15} - \frac{4}{15} = \frac{1}{15}$.Total filled in 3 hours $= \frac{1}{3} + \frac{1}{5} + \frac{1}{15} = \frac{9}{15} = \frac{3}{5}$.Hence, fraction still to be filled $= 1 - \frac{3}{5} = \frac{2}{5}$.Answer:$\frac{2}{5}$, i.e. Option C.