A and B can complete a workin 20 days .B and C can complete the same work in 24 days.The work was started by A and he work for 8 days,then after B wors for 11 days and the C completes the remaining work in 22 days,then the number of days required for c alone to complete the work is

Let the total work be 120 units and let the per day capacities of A,B,C be a, b, c units

Hence,
a + b = 6 ..... (A)
b + c = 5 ..... (B)

Hence, a + 2b + c = 11 ..... (C) & a - c = 1 ..... (D)
Also, given that:
8a + 11b + 22c = 120 ..... (E) 

Multiplying (A) by 6 and (B) by 5, adding both, we get 6a + 11b + 5c = 61 ..... (F) 
Subtracting (F) from (E), we get: 2a + 17c = 59 ..... (G) 

Multiplying (D) by 2, subtracting from (G), we get
19c = 57 
c = 3 

Hence, C alone takes 120/3 = 40 days to complete work