if A and B works together then they complete the work in 12 days

1/A+1/B=1/12------>(eqn 1)

if B and C works together then they complete the work in 20/3 days

1/B+1/C=3/20------>(eqn 2)

Now,

A works for 3 days and B works for 4 days and C works for 7 days so the equation for this

3/A+4/B+7/C=1

Substitute the value of 1/A and 1/C from equation 1 and 2 then we get,

3(1/12-1/B)+4/B+7(3/20-1/B)=1

1/B=1/20

now put 1/B=1/20 in equation 1 so we get,

1/A=1/30

that means A alone can complete the work in 30 days.