A B and C together can finish a piece of work in 12 days A and C together work twice as much as B ,A and B together work thrice as much as C.In what time in days could each do it separately.
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Step-by-step explanation:
Let A's 1 day work = a
B's 1 day work = b
C's 1 day work = c
∴A+B+C=
12
1
...(1)
A+C=2B ...(2)
A+B=3C ...(3)
From(2)
A=2B−C ...(4)
from (3)
A=3C−B ...(5)
comparing (4) and (5)
2B−C−3C−B
3B=4C
B=
3
4
C ...(6)
putting in (5)
A=BC−
3
4C
A=
3
5C
...(7)
putting (6) and (7) in (1)
3
5C
+
3
4C
+C=
12
1
3
12C
=
12
1
C=
48
1
∴A=
3
5
×
48
1
=
144
5
B=
3
4
×
48
1
=
36
1
∴ A finishes in
5
144
days
B finishes in 36 days
C finishes in 48 days
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