# A and B can do a piece of work in 15 days; B and C can do it in 12 days while C and A can finish it 20 days; in how many days will A,B,C finish it working together?

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10 days.

A, B , C can complete the work in a, b , c days respectively by working alone.

1/a + 1/b = 1/15 1/b + 1/c = 1/12 1/c + 1/a = 1/20

Add these equations : 2 [ 1/a + 1/b + 1/c ] = 1/15 + 1/12 + 1/20 = 1/5

1/a + 1/b + 1/c = 1/10

A, B,C can do 1/10 work per day. so 10 days to complete.

A, B , C can complete the work in a, b , c days respectively by working alone.

1/a + 1/b = 1/15 1/b + 1/c = 1/12 1/c + 1/a = 1/20

Add these equations : 2 [ 1/a + 1/b + 1/c ] = 1/15 + 1/12 + 1/20 = 1/5

1/a + 1/b + 1/c = 1/10

A, B,C can do 1/10 work per day. so 10 days to complete.