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A painting job can be completed by 6 painters in 35 days. If 18 more painters join the team 7 days after starting work on the job, then how many more days are required to complete the job?
Answer: 7
Solution:
Total effort required by 6 painters for 35 days = 6 × 35 = 210 man-days.
Initial effort by 6 painters for 7 days = 6 × 7 = 42 man-days.
Job still requires 210 − 42 = 168 man-days, and there are 24 painters available to do it.
Additional effort required by 24 painters for 168 man-days = 168 / 24 = 7 days.
Thus, 7 more days are required to complete the painting job.
Alternative Shorter Solution:
6 painters require 35 − 7 = 28 more days to complete the job.
Therefore, 6 + 18 = 24 painters will require 28 × 6 / 24 = 7 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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