AFCAT Model Paper 1

Given: Time taken by Ramesh and Rajesh to do the work together = 12 days Calculation: Let the time taken by Ramesh and Rajesh to do the work alone be x and y respectively. Then, Ramesh’s and Rajesh’s 1 day work is equal to $\frac{1}{x}$ and $\frac{1}{y}$ respectively ⇒ $\left(\frac{1}{x}\right) + \left(\frac{1}{y}\right) = \frac{1}{12}$ ...(i) Ramesh reduced his efficiency by half then time taken to complete the work by both of them is increased by 50%. ⇒ Ramesh’s 1 day work $= \frac{1}{2x}$ ⇒ Time taken by them to finish the work $= 12 \times \left(\frac{150}{100}\right) = 18$ days ⇒ $\frac{1}{2x} + \frac{1}{y} = \frac{1}{18}$ ...(ii) Solving (i) and (ii) x = 18 and y = 36 ∴ Time taken by Rajesh to finish the work alone is 36 days