Multiple choice

2 men and 3 women can finish a piece of work in 10 days, while 4 men can do it in 10 days. In how many days will 3 men and 3 women finish it?

  1. 6 days

  2. 5 2/3 days

  3. 8 days

  4. 81/3 days

  5. 10 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

4 men = 10 days, so 1 man = 40 days. 2 men + 3 women = 10 days. 2*(1/40) + 3*(1/W) = 1/10. 1/20 + 3/W = 1/10. 3/W = 1/20. W = 60 days. 3 men + 3 women = 3*(1/40) + 3*(1/60) = 9/120 + 6/120 = 15/120 = 1/8. Time = 8 days.

AI explanation

Using the LCM method, let the total work be the least common multiple of 10 and 10, which is 10 units. The equation (2 Men + 3 Women) = 1 unit per day and (4 Men) = 1 unit per day reveals that 2 Men equal 3 Women in daily work capacity. Substituting this into the first equation means that 4 Men equal 1 unit of work per day, making the capacity of 3 Men and 3 Women equal to 1.25 units per day. To complete the 10 units of work at a rate of 1.25 units per day, it will take 10 / 1.25 = 8 days.

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