Here, A worked for 5 days, B for 7 days and C for 13 days = (A + B) worked for 5 days, (B + C) for 2 days and C for 11 days. Let C will complete the work in x days, Now, (A + B)'s 5 days' work + (B + C)'s 2 days' work + C's 11 days' work =
5
12
+
2
16
+
11
x
=
13
24
+
11
x
Again,
13
24
+
11
x
= 1 ⇒
11
x
=
11
24
∴ x = 24 Hence, C would alone complete the work in 24 days.