MAT Exam 2021 Paper

Concept:Efficiency is inversely proportional to time taken. Work done in $1$ day is the efficiency of a worker.Explanation:Let efficiency of $A$ be $5x$ and efficiency of $C$ be $3x$.Since $A$ takes 6 days less than $C$ to complete the work,$$\frac{1}{3x} - \frac{1}{5x} = 6$$$$\frac{2}{15x} = 6$$$$\frac{1}{x} = 45$$So, time taken by $A = \frac{1}{5x} = \frac{45}{5} = 9$ days.Time taken by $C = \frac{1}{3x} = \frac{45}{3} = 15$ days.Given, days ratio of $B$ and $C$ is $2 : 3$.Time taken by $B = \frac{2}{3} \times 15 = 10$ days.One day work of $B$ and $C$ together:$$\frac{1}{10} + \frac{1}{15} = \frac{1}{6}$$Work done by $B$ and $C$ in 2 days:$$2 \times \frac{1}{6} = \frac{1}{3}$$Remaining work:$$1 - \frac{1}{3} = \frac{2}{3}$$Time taken by $A$ to finish remaining work:$$\frac{2}{3} \times 9 = 6 \text{ days}$$Answer:$6$ daysOption C.