Multiple choice

X and Y can do a piece of work in 45 days and 40 days, respectively. They begin to work together, but X leaves after n days and then Y completes the remaining work in 23 days. What is n equal to?

  1. 8

  2. 9

  3. 10

  4. 12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

X does 1/45 per day, Y does 1/40 per day. Together for n days: n(1/45 + 1/40) = n(8+9)/360 = 17n/360. Y works alone for 23 days: 23/40 = 207/360. 17n/360 + 207/360 = 1. 17n = 360 - 207 = 153. n = 153/17 = 9.

AI explanation

Using the LCM method, assume the total job is 360 units (the least common multiple of 45 and 40). X's daily output is 8 units and Y's daily output is 9 units. Y labored alone for 23 days to finish the job, completing 23 * 9 = 207 units. The remaining 360 - 207 = 153 units were completed by X and Y together. Their combined daily output is 8 + 9 = 17 units, so they worked together for 153 / 17 = 9 days. Thus, n equals 9.

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