Given:
Time taken by A alone to complete the work: 12 days
Time taken by A and B together to complete the same work: 8 days
Concept:
If a task is being done in collaboration, then the combined rate of work is the sum of the individual rates.
Solution:
Let's assume that the total work to be done is 1 unit. Then, the rate at which A completes the work is:
⇒ Rate of A = Total work / Time taken by A = 1 / 12 = 0.0833 units/day
The combined rate at which A and B together complete the work is:
⇒ Combined rate of A and B = Total work / Time taken by both A and B = 1 / 8 = 0.125 units/day
Thus, the rate at which B completes the work (Rate of B) is the difference between the combined rate and A's rate:
⇒ Rate of B = Combined rate of A and B - Rate of A = 0.125 - 0.0833 = 0.0417 units/day
Finally, the time taken by B to complete the work alone is the total work divided by B's rate:
⇒ Time taken by B = Total work / Rate of B = 1 / 0.0417 = 24 days
Therefore, B alone can complete the work in 24 days.