Question

10 workers working 6 hours a day prepare 12,600 articles in 15 days . How many articles will 8 workers working 7 hours a day prepare in 12 days ?

Answer 1

We know this:

12 men : 8 hours/day : 10 days

x men : 15 hours/day: 8 days

Lets try and reduce the number of variables which can be done if we eliminate a common factor between the two.

For this lets see how many days 12 men would take to complete the work if they worked 15 hours instead of 8.

Now we know that if 12 men work harder, they will complete work quicker. So the rate of work and the duration are inversely proportional.

So 8 h/d : 10

15 h/d : y days

Then y = 8 *10/15 = 80/15 = 16/3 days.

Now we can refactor the first set of equations as :

12 : 15 : 16/3

x : 15 : 8

We can eliminate 15 because its the same.

12 : 16/3

x : 8

Since x men take more time than 12 men, x must be lesser than 12.

Therefore

8*x = 12 * 16/3


or

x = 12 * 2/3 = 8 men.
this is an example