Multiple choice

$2$ women and $5$ men can together finish an embroidery work in $4$ days, while $3$ women and $6$ men can finish it in $3$ days. Find the time taken by $1$ woman as well as $1$ man to finish the work if each of them works alone.

  1. Time taken by $1$ woman alone to finish the work: $24$ days, and also that taken by $1$ man alone: $32$ days
  2. Time taken by $1$ woman alone to finish the work: $18$ days, and also that taken by $1$ man alone: $36$ days
  3. Time taken by $1$ woman alone to finish the work: $14$ days, and also that taken by $1$ man alone: $30$ days
  4. Time taken by $1$ woman alone to finish the work: $12$ days, and also that taken by $1$ man alone: $28$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let W be the work of a woman and M be the work of a man per day. 2W + 5M = 1/4 and 3W + 6M = 1/3. Solving this system of linear equations yields W = 1/18 and M = 1/36. Thus, a woman takes 18 days and a man takes 36 days.

AI explanation

Let a woman's daily work be W and a man's daily work be M. The given conditions translate to 2W + 5M = 1/4 and 3W + 6M = 1/3. Solving this system of equations yields W = 1/18 and M = 1/36. Therefore, a woman alone takes 18 days and a man alone takes 36 days to complete the work.

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