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A painting job can be completed by 4 painters in 10 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? Answer: 2
**Solution:**
Total effort required by 4 painters for 10 days = 4 × 10 = 40 man-days.
Initial effort by 4 painters for 4 days = 4 × 4 = 16 man-days.
Job still requires 40 − 16 = 24 man-days, and there are 12 painters available to do it.
Additional effort required by 12 painters for 24 man-days = 24 / 12 = 2 days.
Thus, 2 more days are required to complete the painting job.
**Alternative Shorter Solution:**
4 painters require 10 − 4 = 6 more days to complete the job.
Therefore, 4 + 8 = 12 painters will require 6 × 4 / 12 = 2 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?
Try the Quiz : __Puzzles & Brain Teasers : Painting Job__
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