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July 20th, 2019, 08:14 PM   #1
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Why n-4 in first step?

Q. A group of men can complete a work in 24 days. In first 13 days, they all work together and then after every day 2 men left. If the work would be completed in 27 days, what was the total number of men in that group?

Shortcut: 24n=13n+n-2+n-4----14 days
24n=13n+14/2(2n-4-26)

24n=13n+7(2n-30)
24n=13n+14n-210
3n=210
n=70

Why n-4 in first step?

Last edited by skipjack; July 21st, 2019 at 02:00 AM.
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July 20th, 2019, 09:33 PM   #2
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In second step: 24n=13n+14/2(2n-4-26)

How 14/2(2n-4-26) is written??
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July 21st, 2019, 03:20 AM   #3
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Each day, 2 men left. If that means that 2 men left just before (or as) day 14 commenced, n - 2 men worked on day 14, n - 4 men worked on day 15, and so on until n - 28 men worked on day 27.

It would be clearer to write (n - 2) + (n - 28), but 2n - 4 - 26 is an equivalent expression.
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