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A painting job can be completed by 8 painters in 24 days. If 8 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: 9
Solution:
Total effort required by 8 painters for 24 days = 8 × 24 = 192 man-days.
Initial effort by 8 painters for 6 days = 8 × 6 = 48 man-days.
Job still requires 192 − 48 = 144 man-days, and there are 16 painters available to do it.
Additional effort required by 16 painters for 144 man-days = 144 / 16 = 9 days.
Thus, 9 more days are required to complete the painting job.
Alternative Shorter Solution:
8 painters require 24 − 6 = 18 more days to complete the job.
Therefore, 8 + 8 = 16 painters will require 18 × 8 / 16 = 9 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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