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A painting job can be completed by 8 painters in 35 days. If 24 more painters join the team 3 days after starting work on the job, then how many more days are required to complete the job?
Total effort required by 8 painters for 35 days = 8 × 35 = 280 man-days.
Initial effort by 8 painters for 3 days = 8 × 3 = 24 man-days.
Job still requires 280 − 24 = 256 man-days, and there are 32 painters available to do it.
Additional effort required by 32 painters for 256 man-days = 256 / 32 = 8 days.
Thus, 8 more days are required to complete the painting job.
Alternative Shorter Solution:
8 painters require 35 − 3 = 32 more days to complete the job.
Therefore, 8 + 24 = 32 painters will require 32 × 8 / 32 = 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