Mowing a lawn 5 acres in size is part of a community service project. A group of people, including boys, girls, ladies and men, take up the job. They continue until the job is done. It is assumed that the job is the same regardless of how many days taken: i.e., there is no appreciable growth of grass.

a) 3 boys and 8 ladies can do the job in 3 days.
b) 8 girls & 2 men can do it in 4 days, which is the same as the time taken by 2 men and 6 boys.
c) 3 boys can do the job as fast as 2 men.

One day they reach the place of work and find that there are four bowls containing pills kept for each category. (Marked- Boys, Girls, Ladies & Men). Two of these bowls contain poison pills and two contain energy pills. After consuming a poison pill their rate reduces to one third and after consuming an energy pill their rate becomes double.

In all, eight persons are present and there is at least one member from each category. They each take one pill from their respective bowl and start working. The job was completed in 6 days and the number of girls is not more than the number of boys. How many boys, girls, ladies and men were present and which pill did they have?

The 8 people consisted of  4 ladies and 2 men, who all took poison pills, and 1 boy and 1 girl, who each took energy pills.

I converted the statements into rates of work and came up with the following:

Person  On Poison Pill   On Energy Pill
---------------------------------------
Boy       40/4320          240/4320
Girl      30/4320          180/4320
Man       60/4320          360/4320
Lady      45/4320          270/4320

* The rates indicate how much of the field each person could mow in one day.

It took just a minute of fiddling with the numbers to find a solution that worked.  If it took them 6 days, I was looking for a combination of 8 people that would total a rate of 1/6 or 720/4320 per day.

This works out to:

4 ladies (on poison pills) = 4 *  45/4320 = 180/4320
2 men (on poison pills)    = 2 *  60/4320 = 120/4320
1 boy (on energy pills)    = 1 * 240/4320 = 240/4320
1 girl (on energy pills)   = 1 * 180/4320 = 180/4320
                                            --------
                                            720/4320

Posted by tomarken on 2006-05-23 15:34:19