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A and B can do a piece of work in 12 days, B and C in 15 days and C and A in 20 days. In how many days will they finish it together and separately.
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Explanation:
(A+B)’s one day work = 1\12
(B+C)’s one day work = 1\15
(C+A)’s one day work = 1\20
2(A+B+C)’s one day work = 1\10+1\15+1\20=25+20+15\300=60\300=1\5
(A+B+C)’s one day work = 1\10 …(1)
A, B, C can do the work in 10 days.
A’s one day work = (A+B+C)’s one day work – (B+C)’s one day work
= 1\10−1\15=15−10\150=5\150=1\30
A can do the work in 30 days. …(2)
B’s one day work = (A+B+C)’s one day work – (A+C)’s one day work
= 1\10−1\20=10−5\100=5\100=1\20
B can do the work in 20 days. …(3)
C’s one day work = (A+B+C)’s one day work – (A+B)’s one day work
= 1\10−1\12=12−10\120=2\120=1\60
C can do the work in 60 days.