Multiple choice

4 women and 5 men can complete a certain work in X days, while 4 men and 1 woman can complete the same work in Y days. The work completed by 1 man in 1 day is 250% of the work completed by 1 woman in 1 day. Which of the following is the ratio of the number of days required to complete the work by 4 women and 5 men together and the number of days required to complete the work by 4 men and 1 woman together? (i) 5 : 3 (ii) 2 : 3 (iii) 4 : 3 (iv) 6 : 5

  1. Only (i)

  2. Only (ii)

  3. Only (iii)

  4. Only (iv)

  5. None of these
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B Correct answer
AI explanation

Let the daily work of 1 woman be W, making the daily work of 1 man equal to 250 percent of W, which is 2.5W. The daily work of 4 women and 5 men becomes 4W plus 12.5W, totaling 16.5W, while the daily work of 4 men and 1 woman becomes 10W plus W, totaling 11W. Because the time taken to complete the work is inversely proportional to the daily work rate, the ratio of the time taken by the first group to the second group is 11W to 16.5W, which simplifies to 2 to 3.

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