if 20% of a certain quantity of work is done by A abd after that the remaining 80% of work is done by B the work will be completed in 20 days if 80% of the work is done by A and after that the remaining 20 % of tge work is done by B the work will be completed in 30 days how many days are required to complete the work if A and B work together?
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Let,
A take 'a' days to complete 100% work.
B take 'b' days to complete 100% work.
I. 20% by A and 80% by B :
20% of work by A => A took a/5 days
80% of work by B => B took 4b/5 days
So, (a/5) + (4b/5) = 20
=> a+4b = 100 ---->(1)
II. 80% by A and 20% by B :
80% of work by A => A took 4a/5 days
20% of work by B => B took b/5 days
So, (4a/5) + (b/5) = 30
=> 4a+b = 150 ---> (2)
Solving (1) and (2), we get ,
a = 100/3 days , b = 50/3 days
A's one-day work = 3/100 and B's one-day work = 3/50
Thus, A and B's one-day work (combined) = 3/100 + 3/50 = 9/100
Thus they would take 100/9 = 11 1/9 days to complete the work.
Regards,
KKKoppu
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