X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone, and then after 4 days, Y joined him until the completion of the work. How long did the work last?
Answer: 10 days
Explanation
X can do the work in 20 days, so X's work rate is 1/20 of the work per day.
Y can do the work in 12 days, so Y's work rate is 1/12 of the work per day.
X works alone for 4 days, completing 4/20 = 1/5 of the work.
Y joins X, and together they complete the remaining 4/5 of the work.
Their combined work rate is (1/20 + 1/12) = 8/60 = 2/15 of the work per day.
Since they complete 4/5 of the work together, it takes them (4/5) / (2/15) = 6 days to complete the remaining work.
Adding the 4 days X worked alone, the total duration is 4 + 6 = 10 days.
So, the correct answer is: 10 days.
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