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A painting job can be completed by 7 painters in 46 days. If 28 more painters join the team 6 days after starting work on the job, then how many more days are required to complete the job?
Answer: 8
Solution:
Total effort required by 7 painters for 46 days = 7 × 46 = 322 man-days.
Initial effort by 7 painters for 6 days = 7 × 6 = 42 man-days.
Job still requires 322 − 42 = 280 man-days, and there are 35 painters available to do it.
Additional effort required by 35 painters for 280 man-days = 280 / 35 = 8 days.
Thus, 8 more days are required to complete the painting job.
Alternative Shorter Solution:
7 painters require 46 − 6 = 40 more days to complete the job.
Therefore, 7 + 28 = 35 painters will require 40 × 7 / 35 = 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?
Try the Quiz : Puzzles & Brain Teasers : Painting Job
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