How to solve this confusing question? 100 cows can graze a field completely in 15 days, while 60 cows can do it in 30 days. How many cows are needed to do it in 10 days? Answer is 140 cows I tried: It'd seem like it'd only take 50 cows to graze a field in 30 days if 100 can do it in 15. But in question it shows 60 cows can do it in 30 days. I am confused with this question. 
You have to take account of the grass growing during the grazing time. 
Let c be the fraction of a field that a cow grazes in a day. Let g be the fraction of a field that grows in a day, and assume that g is a constant. You can now write two equations: 15(100c  g) = 1 and 30(60c  g) = 1. Solving those gives c = 1/1200 and g = 1/60. If n cows can graze the field completely in 10 days, 10(n/1200  1/60) = 1, so n = 120(1 + 1/6) = 140. 
Beer soaked counter questions follow. Quote:
A man can drink a cask of wine in 20 days, but if his wife drinks with him it will take only 14 daysâ€”how long would it take for the wife alone? If one priest can pray a soul out of purgatory in 5 hours, while it takes a second priest 8 hours, how long will it take if the two priests prayed together? 
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why 1 after "equal to" sign ? why not 2,3, 50,100? 
The "1" is because 1 field is grazed in the 15 days (or 30 days for the second equation). 
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As an aside: if grass grows constantly, field will never be "completely" grazed! 
Every cow was Kung Fu grazing, Those cattle were faster than lightning! In fact, it was a little bit frightening... But they mowed with expert timing! 
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