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May 28th, 2019, 11:24 AM  #1 
Member Joined: Feb 2018 From: Iran Posts: 50 Thanks: 3  Compound proportion
If 8 workers work 6 hour a day and dig 6 holes of 18 meter depth in 27 days then how many holes of 24 meter depth can 12 workers that work 8 hour a day dig in 12 days? Please explain step by step 
May 28th, 2019, 12:33 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
If the number of workers is multiplied by 12/8, the number of hours worked per day is multiplied by 8/6, and the number of days worked by each worker is multiplied by 12/27, it seems reasonable to calculate that 12 workers who work 8 hours a day for 12 days can dig 6 × 12/8 × 8/6 × 12/27 holes of 18 meter depth. That 16/3 holes. If the holes need to be 24 meters deep, instead of 18 meters deep, let's assume that it's necessary to multiply by 18/24. As 16/3 × 18/24 = 4, the final answer is 4. 

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