Solution: suppose that a, b and c need x, y, z, y, z days to work alone,

A 1/x, b 1/y and c 1/z of the total task every day.

5 *( 1/x+ 1/y)= 1/3

2 * (1/y+1/z) = (1-1/3) *1/4, that is, 1/6.

5 * (1/x+1/z) =1-1/3-1/6, that is, 1/2.

The simultaneous solutions are 1/x = 1/24, 1/y = 1/40, 1/z = 7/ 120.

x=24，y=40，z= 120/7

A: It takes 24 days, 40 days and 120/7 days for Party A, Party B and Party C to work alone.