Given,

A, B and C can reap the field in = 15 days

B, C and D can reap it in = 14 days

C, D and A can reap it in = 18 days

D, A and B can reap it in = 21 days

So,

A, B and C’s 1 day work =

B, C and D’s 1 day work =

C, D and A’s 1 day work =

D, A and B’s 1 day work =

Now, adding up,

3[A+B+C+D] =

A+B+C+D =

Thus A, B, C, D can finish the work in = days.