A job can be done by 15 men in 30 days. In how many days can 12 men complete the
job, given that the time spent per day is decreased by 1/4th the previous time?
In this problem we have long days and short days.
the time spent per day is decreased by 1/4th the previous time
1 short day = 3/4 long day.
Multiply both sides by 4/3
4/3 short day = 1 long day
A job can be done by 15 men in 30 (LONG) days.
So 30 long days is the same as 4/3*30 or 40 short days.
So 15 men can do 1 job in 40 short days.
So 1 man will take 15 times as long or 15*40 or 600 short days.
So the rate of 1 man is 1 job per 600 short days or 1/600 job per
short day.
So the rate of 12 men is 12 times that rate or 12/600 job per short day.
That reduces to 1/50 job per short day. So it'll take them 50 short days.
Edwin