Multiple choice

In how many days can $10$ women finish a work? $I$. $10$ men can complete the work in $6$ days. $II$. $10$ men and $10$ women together can complete the work in $3\cfrac{3}{7}$ days. $III$. If $10$ men work for $3$ days and thereafter $10$ women replace them, the remaining work in completed in $4$ days.

  1. Any two of the three
  2. $I$ and $II$ only
  3. $II$ and $III$ only
  4. $I$ and $III$ only

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M be men's rate, W be women's rate. I: 10M = 1/6. II: 10M + 10W = 1/(24/7) = 7/24. III: 10M*3 + 10W*4 = 1. Any two of these equations allow solving for M and W, thus finding the time for 10 women (1/W).

AI explanation

Let M be the daily work rate of one man and W be the daily rate of one woman, with the total work being 1. Statement I gives the equation 60M = 1; statement II gives the equation (24/7)(10M + 10W) = 1; statement III gives the equation 30M + 40W = 1. Taking any two of these three statements provides a system of two distinct linear equations that can be solved simultaneously to find W and calculate the 10 women's completion time. For example, combining I and II yields W = 1/120, meaning 10 women would take 12 days. Therefore, any two of the three statements are sufficient to answer the question.

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