MAT Exam 2023 Paper

Concept:If Amar is thrice as good a workman as Vikram, Amar’s time is $\frac{1}{3}$ of Vikram’s time.Explanation:Let Vikram alone take $x$ days to complete the work.Then Amar alone takes $x - 80$ days.Since Amar’s time : Vikram’s time $= 1 : 3$,$x - 80 = \frac{x}{3}$$3x - 240 = x$$2x = 240$, so $x = 120$ days.Hence Vikram takes $120$ days and Amar takes $40$ days.Work done by both in one day:$\frac{1}{120} + \frac{1}{40} = \frac{1 + 3}{120} = \frac{4}{120} = \frac{1}{30}$So together they can finish the work in $30$ days.Answer:$30$ days, i.e. option D.