Multiple choice

$X$ and $Y$ can do a piece of work in $30$ days. They work together for $6$ days and then $X$ quits and $Y$ finishes the work in $32$ more days. In how many days can $Y$ do the piece of work done?

  1. $30\ days$
  2. $32\ days$
  3. $10\ days$
  4. $40\ days$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

X+Y = 1/30 work/day. In 6 days, they do 6/30 = 1/5 work. Remaining = 4/5 work. Y does 4/5 work in 32 days, so Y's rate = (4/5) / 32 = 1/40 work/day. Y takes 40 days to finish the work.

AI explanation

Let the total work be the product of 30 days and their combined rate, which we can set to 1, making their combined rate 1/30 per day. In 6 days of working together, X and Y complete 6/30 or 1/5 of the work, leaving 4/5 of the work remaining. Y finishes this 4/5 of the work in 32 days, meaning Y's daily work rate is (4/5) divided by 32, which equals 1/40. By subtracting Y's rate from their combined rate, X's rate is found to be 1/30 minus 1/40, and the question asks for Y's time which is 40 days.

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