MAT Exam 2024 Paper

Concept:Let the planned daily output be $x$ pieces. The time is found by comparing the planned time with the actual time at the increased rate.Explanation:Planned number of days $= \frac{360}{x}$.New daily output $= x + 4$ pieces.New number of days $= \frac{360}{x + 4}$.Since the work is completed 1 day earlier, we write:$$\frac{360}{x} - \frac{360}{x + 4} = 1$$Solving:$$\frac{360(x+4)-360x}{x(x+4)}=1$$$$\frac{1440}{x(x+4)}=1$$$$x^2 + 4x - 1440 = 0$$$$x^2 + 40x - 36x - 1440 = 0$$$$(x+40)(x-36)=0$$So, $x = 36$ pieces per day, since $x = -40$ is not possible.New daily output $= 36 + 4 = 40$ pieces.Days required under the new planning:$$\frac{360}{40} = 9 \text{ days}$$Answer:Option B. 9 days.