$16$ men or $24$ women can do a piece of work in $20$ days. The number of days needed to complete the job, if $20$ men and $30$ women are employed to do the same piece of work is

Let the total work be the LCM of 16 and 24, which is 48 units. Since 16 men or 24 women take 20 days, the daily rate of 16 men is 48 divided by 20, or 2.4 units, meaning 1 man does 0.15 units per day. Similarly, the daily rate of 24 women is 2.4 units, so 1 woman does 0.1 units per day. Employing 20 men and 30 women gives a daily output of 20 times 0.15 plus 30 times 0.1, which equals 6 units. Dividing the 48 total units by 6 units per day results in 8 days.

• Thanks
• Wrong explanation