Multiple choice

6 men and 8 women can complete a job in 20 days, while 8 men and 22 women can complete it in 10 days. Find the time taken by 34 women to complete the same job.

  1. 10 days

  2. 12 days

  3. 15 days

  4. 18 days

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

Let M and W be the work done by one man and one woman per day. 20(6M + 8W) = 10(8M + 22W). 120M + 160W = 80M + 220W. 40M = 60W, so 2M = 3W. Total work = 20(6M + 8(2/3)M) = 20(6M + 16/3 M) = 20(34/3 M) = 680/3 M. Time for 34 women = (680/3 M) / (34 * 2/3 M) = 680 / 68 = 10 days.

AI explanation

Let m be one man's one-day work and w be one woman's one-day work. From the given information, 6m + 8w = 1/20 and 8m + 22w = 1/10. Multiplying the first equation by 4 yields 24m + 32w = 1/5, and multiplying the second equation by 3 yields 24m + 66w = 3/10. Subtracting the first modified equation from the second gives 34w = 3/10 - 1/5 = 1/10, which means 34 women complete 1/10 of the work in one day. Therefore, 34 women will complete the entire job in 10 days.

Keep practicing — related questions