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July 24th, 2019, 08:11 AM   #1
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How to solve this time & work problem?

24 men can complete a work in 16 days. 32 women can complete the same work in 24 days. 16 men & 16 women started working and worked for 12 days. How many more men are to be added to complete the remaining work in 2 days?

Sol: 24m → 16
32w → 24

24m*16 = 32w*24
1m=2w

Total work done by 24men in 16 days = 24*16 = 384.

16m + 16w In 12 days.
Since 1m=2w, 16m + 8m i.e 24m.

Total work done for 12 days = 24m*12 = 288
Remaining work = 384 – 288 = 96.

After this how to proceed?
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July 24th, 2019, 08:24 AM   #2
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By adding units (even fictitious and sexist ones), it may become clearer.

1 job = (24 men)*(16 days) = 384 man*days.
Work done = (16 men)*(12 days) + (16 women)*(1 man/2 women)*(12 days) = 288 man*days (= 0.75 job).
Work remaining = 384 - 288 = 96 man*days

You need 96 man*days of work done in 2 days. How many total "equivalent men" do you need?
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July 24th, 2019, 08:33 AM   #3
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Quote:
Originally Posted by DarnItJimImAnEngineer View Post
Work done = (16 men)*(12 days) + (16 women)*(1 man/2 women)*(12 days) = 288 man*days (= 0.75 job).
What is 0.75 job means?

Extra 48 men required is the answer ?

Last edited by Ganesh Ujwal; July 24th, 2019 at 08:38 AM.
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July 24th, 2019, 08:42 AM   #4
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Quote:
Originally Posted by Ganesh Ujwal View Post
24 men can complete a work in 16 days.
I defined "a work" = 384 man*days = 1 "job."

Not extra 48 men, but the equivalent of 48 men total. Accounting for the men and women already working, how many more will you need?
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July 24th, 2019, 08:51 AM   #5
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Quote:
Originally Posted by DarnItJimImAnEngineer View Post
I defined "a work" = 384 man*days = 1 "job."

Not extra 48 men, but the equivalent of 48 men total. Accounting for the men and women already working, how many more will you need?
Actual answer is 24. We already separated women by replacing with men in equations. why still we have consider women again ?

If they ask how many women & men needed for last 2 days, then how should I proceed?

Last edited by Ganesh Ujwal; July 24th, 2019 at 09:30 AM.
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July 24th, 2019, 09:46 AM   #6
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Mathematically, you don't. Physically, though, one man is not the same thing as two women. That's why I said the men and women already working. We have the equivalent of 24 men already, so 24 more are needed.

If you weren't constrained to hiring only men, you would have multiple options. You could hire 24 men, or 23 men and 2 women, or 22 men and 4 women, etc..
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July 24th, 2019, 06:10 PM   #7
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Quote:
Originally Posted by DarnItJimImAnEngineer View Post
That's why I said the men and women already working. We have the equivalent of 24 men already, so 24 more are needed.
Does it mean old 24 men can't complete the remaining work in 2 days?
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