A can complete 40% of a work in 6 days and B can complete 33
3
1
​
% of the same work in 8 days. They work together for 8 days. C alone completes the remaining work in 4 days. A and C together will complete the same work in:

Total days needed by A and B to finish the work:
A completes 40% (
5
2
​
) of the work in 6 days → Total days for A =6×
2
5
​
=15 days.

B completes 33
3
1
​
% (
3
1
​
) of the work in 8 days → Total days for B =8×3=24 days.

Let the total work be the LCM of 15 and 24, which is 120 units.

Efficiencies:

Efficiency of A =
15
120
​
=8 units/day

Efficiency of B =
24
120
​
=5 units/day

Combined efficiency of A and B =8+5=13 units/day.

Work completed by A and B in 8 days:

Work done=13×8=104 units
Remaining work:

Remaining work=120−104=16 units
C completes this remaining work in 4 days:

Efficiency of C=
4
16
​
=4 units/day
Combined efficiency of A and C =8+4=12 units/day.

Time taken by A and C together to complete the entire work:

Time=
12
120
​
=10 days