a can complete a work in 10 days B in 12 days and C in 15 day all of them begin the work together but I had to leave the work after two day of the start and B three day before the completion of the work how long did the work last
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Step-by-step explanation:
Given A can do the work in 10 days ,B can do the work in 12 days and C can do the work in 15 days.
Then A's one day's work =
10
1
B's one day's work =
12
1
C's one day's work =
15
1
Then (A+B +C)'s one day's work =
10
1
+
12
1
+
15
1
=
1800
450
=
4
1
(A+B+C)'s two days' work =
4
1
×2=
2
1
But B leaves 3 days before the work gets finished, so C does the remaining work alone
C's 3 days' work =
15
1
×3=
5
1
Then work done in 2+3 days =
2
1
+
5
1
=
10
7
Work done by B+C together =1−
10
7
=
10
3
(B + C)'s one day work =
12
1
+
15
1
=
20
3
So number of days worked by B and C together=
10
3
×
3
20
=2 days
Then total work done =2+3+2=7 days
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