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Painting Job

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A painting job can be completed by 3 painters in 10 days. If 3 more painters join the team 2 days after starting work on the job, then how many more days are required to complete the job?
Answer: 4

Solution:

Total effort required by 3 painters for 10 days = 3 × 10 = 30 man-days.

Initial effort by 3 painters for 2 days = 3 × 2 = 6 man-days.

Job still requires 30 − 6 = 24 man-days, and there are 6 painters available to do it.

Additional effort required by 6 painters for 24 man-days = 24 / 6 = 4 days.

Thus, 4 more days are required to complete the painting job.

Alternative Shorter Solution:

3 painters require 10 − 2 = 8 more days to complete the job.
Therefore, 3 + 3 = 6 painters will require 8 × 3 / 6 = 4 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?


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puzzle : image for paint

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