Discussion
A can complete a piece of work in 120 days and B can complete it in 150 days. They work together for 20 days. Then B leaves and A alone continues the work. 12 days after that C joins A and the work is completed in 48 more days. In how many days can C complete it if he works alone?
Answer: D
C alone would take 240 days. In 20 days A and B finish 20 × (1/120 + 1/150) = 20 × 9/600 = 0.3. A alone works 12 more days for 12/120 = 0.1. That leaves 1 - 0.4 = 0.6, which A and C finish in 48 days: \[ 48\left(\frac{1}{120} + \frac{1}{c}\right) = 0.6 \] \[ \frac{48}{c} = 0.2 \Rightarrow c = 240 \]
200, 210 and 220 days do not satisfy the equation.
The work completed in the first 20 days (0.3) and the next 12 days (0.1) leaves 0.6 for the final stage of 48 days.
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