SOLUTION: somne persons can do a work in 60 days 8 more mens are added them then can do a work in 50 days ,calculate total no of members

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Question 771672: somne persons can do a work in 60 days 8 more mens are added them then can do a work in 50 days ,calculate total no of members
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Rewriting:
some group of persons can do a job in 60 days. 8 more mes are added to the group. Now, the group can do the same job in 50 days. Calculate total number of members in the original group.

Let n = the number of members in the original group.

Rate for 1 man would be n%2Fn men to do the job in 60%2An days. This can be shown also as 1%2F%2860%2An%29 jobs per day, for ONE man.

Eight more men are added to the group, so n+8 men were able to do the 1 job in 50 days. This rate is 1/50 jobs per day. Also knowing that the n+8 men each have the one-man rate of 1%2F%2860n%29, we can formulate the equation:
highlight%28%28n%2B8%29%281%2F%2860n%29%29=1%2F50%29.

Solve for n in that highlighted equation.
n%2B8=60n%2F50
50n%2B50%2A8=60n
10n=50%2A8
n=5%2A8
highlight%28n=40%29, Forty persons in the original group.