Multiple choice

$X$ can do a piece work in $40$ days. He works at it for $8$ days and then $Y$ finished it in $16$ days. How long will they together take to complete the work?

  1. $13\cfrac{1}{3}$ days
  2. $15$ days
  3. $20$ days
  4. $26$ days
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A Correct answer
Explanation

X does 1/40 of work per day. In 8 days, X does 8/40 = 1/5 of the work. Remaining work = 4/5. Y finishes 4/5 in 16 days, so Y does (4/5)/16 = 1/20 of the work per day. Together, they do 1/40 + 1/20 = 3/40 of the work per day. Time taken = 40/3 = 13 1/3 days.

AI explanation

X works for 8 days at a rate of 1/40 of the work per day, completing 8/40 or 1/5 of the total job. This leaves 4/5 of the work for Y to finish in 16 days, meaning Y's daily work rate is (4/5) divided by 16, which equals 1/20. When X and Y work together, their combined daily rate is 1/40 + 1/20, which totals 3/40 of the work per day. Consequently, they would complete the entire task in the reciprocal of 3/40, which is 13 and 1/3 days.

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