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A painting job can be completed by 4 painters in 28 days. If 8 more painters join the team 4 days after starting work on the job, then how many more days are required to complete the job?
Total effort required by 4 painters for 28 days = 4 × 28 = 112 man-days.
Initial effort by 4 painters for 4 days = 4 × 4 = 16 man-days.
Job still requires 112 − 16 = 96 man-days, and there are 12 painters available to do it.
Additional effort required by 12 painters for 96 man-days = 96 / 12 = 8 days.
Thus, 8 more days are required to complete the painting job.
Alternative Shorter Solution:
4 painters require 28 − 4 = 24 more days to complete the job.
Therefore, 4 + 8 = 12 painters will require 24 × 4 / 12 = 8 more days to complete the job.
Food for thought:
The number of days for the job is inversely proportional to the number of painters. So, is 'number of days × number of painters = constant'?
What assumptions were made to arrive at the solution?
Is something assumed about the output of the painters?
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