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A painting job can be completed by 7 painters in 55 days. If 28 more painters join the team 10 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 7 painters for 55 days = 7 × 55 = 385 man-days.
Initial effort by 7 painters for 10 days = 7 × 10 = 70 man-days.
Job still requires 385 − 70 = 315 man-days, and there are 35 painters available to do it.
Additional effort required by 35 painters for 315 man-days = 315 / 35 = 9 days.
Thus, 9 more days are required to complete the painting job.
Alternative Shorter Solution:
7 painters require 55 − 10 = 45 more days to complete the job.
Therefore, 7 + 28 = 35 painters will require 45 × 7 / 35 = 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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