6 men working for 8 hours can assemble 36 machines. how many machines can be assembled by 4 men working for 4 hours
Answers
Answer:
six men working for 8 hours can assemble 36 machine.how many machines can be assembled by 4 men working for 4 hours?
given:
six men working for 8 hours can assemble 36 machines
to find:
machine can be assembled by 4 men working for 4 hours?
Here goes the problem at the minimum.
8 Men 16 Machines 12 Days
We keep 8 and 15 as is as there’s reversed proportionality and we change 16 and 50 as there’s direct proportionality, and we keep 12 as is anyway and multiply. Please check below:
(8/15)*(50/16)*(12) = (8*50*12) / (15*16)
= (50*12) / (15*2) = (5*12) / 3 = 5*4 = 20 Days.
15 Men 50 Machines ? Days
We need to find the proportionality between Men and No. of Days and Machines and no. of Days.
More men → Fewer Days, this is reversed proportionality, since when 1st quantity is increasing, 2nd quantity is decreasing
More Machines → More Days, This is Direct Proportionality, since when 1st quantity is increasing, 2nd quantity is also increasing
We keep 8 and 15 as is as there’s reversed proportionality and we change 16 and 50 as there’s direct proportionality, and we keep 12 as is anyway and multiply. Please check below:
(8/15)*(50/16)*(12) = (8*50*12) / (15*16)
= (50*12) / (15*2) = (5*12) / 3 = 5*4 = 20 Days.
Unitary method is definitely easy to understand but often involves more steps, as we have to first come down to 1 Unit and then go up to required units. Also in the process, we try to eliminate a few variables, by making them either one or same in both, so that they don’t have any impact on the whole, because they cancel each other.
Direct method gives you direct answer and needless to say, it gives you lot of satisfaction, being slightly complex!
By the way, this (direct) method could be used to solve proportionality problems with more variables also. Normally we have 3 variables and we want to find the value of 4th variable. Here we were having 5 variables and wanted to find the value of 6th variable. Extending this, there could be 2n-1 variables and (2n)th variable value could be found out.