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A painting job can be completed by 5 painters in 19 days. If 20 more painters join the team 9 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 5 painters for 19 days = 5 × 19 = 95 man-days.
Initial effort by 5 painters for 9 days = 5 × 9 = 45 man-days.
Job still requires 95 − 45 = 50 man-days, and there are 25 painters available to do it.
Additional effort required by 25 painters for 50 man-days = 50 / 25 = 2 days.
Thus, 2 more days are required to complete the painting job.
**Alternative Shorter Solution:**
5 painters require 19 − 9 = 10 more days to complete the job.
Therefore, 5 + 20 = 25 painters will require 10 × 5 / 25 = 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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