The given details are,
A, B and C can reap the field in = 15 3/4 days = 63/4 days
(A, B and C)’* 1 day work =1/(63/4) = 4/63
B, C and D can reap the field in = 14 days
B, C and D’* 1 day work = 1/14
C, D and A can reap the field in = 18 days
C, D and A’* 1 day work = 1/18
D, A and B can reap the field in = 21 days
D, A and B’* 1 day work = 1/24
Now adding (A+B+C+D),
3[A+B+C+D] = 4/63 + 1/14 + 1/18 + 1/21
= (8+9+7+6)/126
= 30/126
= 5/21
(A+B+C+D) = 5/(21×3) = 5/63
∴ A, B, C and D together can reap the field in = 1/(5/63) = 63/5 = 12 3/5 days.
