Explanation
Let's assume that A's efficiency is represented by the variable "x" (in terms of the fraction of work done per day) and B's efficiency is represented by the variable "y".
We know that A and B together can complete the work in 8 days. Therefore, their combined efficiency is 1/8 of the work per day.
We also know that A alone can complete the work in 12 days. So, A's efficiency is 1/12 of the work per day.
To find B's efficiency, we subtract A's efficiency from the combined efficiency:
Combined efficiency - A's efficiency = B's efficiency
1/8 - 1/12 = 3/24 - 2/24 = 1/24
Therefore, B's efficiency is 1/24 of the work per day.
To determine how many days B alone would take to complete the work, we can calculate:
1/B's efficiency = 1/(1/24) = 24
Therefore, B alone can complete the work in 24 days.
