Multiple choice

Ten women can complete a piece of work in $15$ days. Six men can complete the same piece of work in $10$ days. In How many days can $5$ women and six men together complete the piece of work?

  1. $15$ days
  2. $7.5$ days
  3. $9$ days
  4. $12.5$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

10 women = 15 days, so 1 woman = 150 days. 6 men = 10 days, so 1 man = 60 days. Work rate of 5 women + 6 men = 5/150 + 6/60 = 1/30 + 1/10 = 4/30 = 2/15. Time = 15/2 = 7.5 days.

AI explanation

Using the LCM method, let the total work be the least common multiple of 15 and 10, which is 30 units. 10 women complete the work in 15 days, so one woman's efficiency is 30 divided by 150, which equals 0.2 units per day. 6 men complete the work in 10 days, so one man's efficiency is 30 divided by 60, which equals 0.5 units per day. The combined efficiency of 5 women and 6 men is 5 times 0.2 plus 6 times 0.5, which equals 1 plus 3, resulting in 4 units per day. Therefore, they will complete 30 units in 30 divided by 4 days, which is 7.5 days.

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