Let’s call the amount of cotton spun by 60 women in 8 hours C. Then we have:
C = 48 kg
The productivity of these workers is:
P1 = C / (60 * 8) = 0.10 kg/hour/woman
This means that each woman, on average, spins 0.10 kg of cotton per hour.
Now let’s consider the situation with 30 women working for 12 hours. Let’s call the amount of cotton spun by these women C’. We want to find C’. Using the same productivity formula, we get:
C’ = P2 * (30 * 12)
where P2 is the productivity of the 30 women.
To find P2, we can use the fact that the productivity is constant. That is, if we double the number of workers, we should double the amount of work done. Similarly, if we double the amount of time, we should also double the amount of work done. Therefore, we can write:
P1 * (60 * 8) = P2 * (30 * 12)
Solving for P2, we get:
P2 = P1 * (60 * 8) / (30 * 12) = 0.10 kg/hour/woman
Plugging this into the formula for C’, we get:
C’ = 0.10 * (30 * 12) = 36 kg
Therefore, 30 women working for 12 hours can spin 36 kg of cotton.