MAT Exam 2023 Paper

Concept:Use the LCM method to assign work units and compare daily work rates of P and Q.Explanation:Let total work be $\mathrm{LCM}(14,21)=42$ units.P’s daily work $=42 \div 14=3$ units.Q’s daily work $=42 \div 21=2$ units.Since P leaves 3 days before completion, Q works alone for the last 3 days.Work done by Q alone in these 3 days $=3 \times 2=6$ units.Remaining work done by P and Q together $=42-6=36$ units.Combined daily work of P and Q $=3+2=5$ units.Time taken together for remaining work $=36 \div 5 = 7\frac{1}{5}$ days.Total time $=3 + 7\frac{1}{5} = 10\frac{1}{5}$ days.Answer:The work is completed in $10\frac{1}{5}$ days.This is not exactly listed among the given options, so the options appear to contain an error.