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A painting job can be completed by 8 painters in 31 days. If 24 more painters join the team 7 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 31 days = 8 × 31 = 248 man-days.
Initial effort by 8 painters for 7 days = 8 × 7 = 56 man-days.
Job still requires 248 − 56 = 192 man-days, and there are 32 painters available to do it.
Additional effort required by 32 painters for 192 man-days = 192 / 32 = 6 days.
Thus, 6 more days are required to complete the painting job.
Alternative Shorter Solution:
8 painters require 31 − 7 = 24 more days to complete the job.
Therefore, 8 + 24 = 32 painters will require 24 × 8 / 32 = 6 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