MAT Exam 2024 Paper

Concept:Each operation causes a net transfer of water from vessel $\mathrm{N}$ to vessel $\mathrm{M}$.Explanation:Pail $\mathrm{A}$ holds $1$ litre.Pail $\mathrm{B}$ holds half as much as $\mathrm{A}$, so it holds $\frac{1}{2}$ litre.In one operation, pail $\mathrm{A}$ transfers $1$ litre from $\mathrm{N}$ to $\mathrm{M}$.Then pail $\mathrm{B}$ transfers $\frac{1}{2}$ litre from $\mathrm{M}$ back to $\mathrm{N}$.So net water gained by $\mathrm{M}$ in one operation is:$$1 - \frac{1}{2} = \frac{1}{2} \text{ litre}$$After $40$ operations, water gained by $\mathrm{M}$ is:$$40 \times \frac{1}{2} = 20 \text{ litres}$$Since the vessels are identical, their water levels become equal when each contains half of the total water.Thus, at equality, $\mathrm{M}$ has $20$ litres and $\mathrm{N}$ also has $20$ litres.Total volume of water in the system:$$20 + 20 = 40 \text{ litres}$$Answer:$40$ litres (Option C).