MAT Exam 2022 Paper

Concept:Use the filling times of pipes C and D to find their per-minute filling rates, then add them alternately.Explanation:From the graph, pipe C fills the cistern in $12$ minutes and pipe D fills it in $4$ minutes.Let the tank capacity be the LCM of $12$ and $4$.So, tank capacity $= 12$ units.Pipe C fills $\frac{12}{12} = 1$ unit per minute.Pipe D fills $\frac{12}{4} = 3$ units per minute.They are opened alternately, starting with pipe C.In the first 2 minutes: C fills $1$ unit and D fills $3$ units, total $4$ units.In the next 2 minutes: again C and D together fill $4$ units.Thus, after $4$ minutes, total filled $= 8$ units.In the 5th minute, pipe C fills $1$ unit, so total becomes $9$ units.In the 6th minute, pipe D fills $3$ units, making total $= 9 + 3 = 12$ units.Hence, the tank is full in $6$ minutes.Answer:D. 6 minutes