AFCAT Model Paper 1

Given: A and S working alone can complete a work in 20 and 30 days respectively Working together, S left the work 5 days before completion. Formula used: The efficiency of a person is the inverse of the time taken Calculation: According to the question: Per day efficiency of $A = \frac{1}{20}$ Per day efficiency of $S = \frac{1}{30}$ Working together, per day efficiency $= \frac{1}{20} + \frac{1}{30}$ ⇒ $\frac{3 + 2}{60} = \frac{5}{60} = \frac{1}{12}$ Let together they worked for d days Then, total work gets completed in d + 5 days ⇒ $\frac{d}{12} + \frac{5}{20} = 1$ ⇒ $\frac{d}{12} = \frac{3}{4}$ ⇒ d = 9 Now, d + 5 = 14 ∴ Total work gets completed in 14 days.