Question

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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Answer 1

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