Final answer:
The work lasted for approximately 13 3/4 days, which is closest to option D - 14 days.
Step-by-step explanation:
To solve this problem, we need to find the individual rates of work for A and B. Let's assume that the total work is represented by the variable W.
We know that A can complete the work in 25 days, so his rate of work is 1/25 of the total work per day. Similarly, B can complete the work in 20 days, so his rate of work is 1/20 of the total work per day.
A started the work and was joined by B after 10 days. So, A worked alone for 10 days and B worked for the remaining days until the work was completed.
Let's calculate the work done by A alone and B alone:
A's work = (A's rate of work) * (number of days A worked) = (1/25) * 10 = 10/25 = 2/5
B's work = (B's rate of work) * (number of days B worked) = (1/20) * (total days - 10) = (1/20) * (25 - 10) = (1/20) * 15 = 3/20
The total work done is the sum of A's work and B's work:
Total work = A's work + B's work = 2/5 + 3/20 = 8/20 + 3/20 = 11/20
The work lasted for 11/20 of the total number of days:
Total number of days = 25
Number of days the work lasted = (11/20) * 25 = 275/20 = 13 3/4 days
So, the work lasted for approximately 13 3/4 days which is closest to option D - 14 days.