The number of workers working on a job increases by 50% and the number of hours they work per day increases by 20%. By what percent should the wage per hour of each worker decrease so that there is no change in the total wage bill per day?

To solve this problem, we need to understand that the total wage bill per day is the product of the number of workers, the number of hours they work, and the wage per hour. If the number of workers and the number of hours increase, the wage per hour must decrease to keep the total wage bill the same.

Here are the steps to solve the problem:

1. Let's assume the initial number of workers is 100, the number of hours they work per day is 10, and the wage per hour is $1. So, the total wage bill per day is 100 workers * 10 hours/worker *$1/hour = $1000.

2. The number of workers increases by 50%, so the new number of workers is 100 workers * 1.5 = 150 workers.

3. The number of hours they work per day increases by 20%, so the new number of hours is 10 hours * 1.2 = 12 hours.

4. We want the total wage bill to remain the same, so we have the equation: 150 workers * 12 hours/worker * new wage/hour = $1000.

5. Solving for the new wage per hour, we get: new wage/hour = $1000 / (150 workers * 12 hours/worker) =$0.5556/hour.

6. To find the percent decrease in the wage per hour, we calculate: (($1 -$0.5556) / $1) * 100% = 44.44%.

So, the wage per hour of each worker should decrease by approximately 44.44% to keep the total wage bill per day the same.