MAT Exam 2025 Paper

Concept:Time and efficiency are inversely proportional. If A is $\frac{5}{2}$ times as efficient as B, then A takes $\frac{2}{5}$ of the time taken by B.Explanation:Let B alone take $x$ days to finish the job.Since A finishes the job in 21 days less than B, A takes $x - 21$ days.The ratio of their times equals the inverse of their efficiency ratio:$\frac{x-21}{x} = \frac{2}{5}$.Cross-multiplying: $5(x - 21) = 2x$.So, $5x - 105 = 2x$, which gives $3x = 105$.Hence, $x = 35$ days. Therefore, B alone takes 35 days.A alone takes $35 - 21 = 14$ days.B's one day's work is $\frac{1}{35}$.A's one day's work is $\frac{1}{14}$.Working together, their one day's work is:$\frac{1}{35} + \frac{1}{14} = \frac{2}{70} + \frac{5}{70} = \frac{7}{70} = \frac{1}{10}$.Thus, together they complete $\frac{1}{10}$ of the job in one day.Answer:Together, they can finish the job in $10$ days. Correct option: C.