A can finish 80% of a task in 12 days and B can finish 20% of the same task in 2 days. They started the task together, but B left after 2 days and A continued to work. In how many days was the entire task completed?

Step 1: Find total time required by A and B individually to complete 100% of the task.
A completes 80% (
5
4
​
) of the task in 12 days.

Total time taken by A=12×
4
5
​
=15 days
B completes 20% (
5
1
​
) of the task in 2 days.

Total time taken by B=2×5=10 days
Step 2: Define total work and efficiencies.
Let Total Work = LCM(15,10)=30 units.

Efficiency of A =
15
30
​
=2 units/day

Efficiency of B =
10
30
​
=3 units/day

Step 3: Calculate work done together in 2 days.
Work done by A and B together in 1 day = 2+3=5 units
Work done in 2 days = 5×2=10 units

Step 4: Calculate remaining work and time taken by A to finish it.
Remaining work = 30−10=20 units
Time taken by A to finish the remaining work =
2
20
​
=10 days

Step 5: Find total time for the entire task.

Total time=Initial 2 days with B+10 days by A alone=12 days