Word Problem No.2 (Compound Proportion) --- Women, Time, and Cotton spin (kg) (Compound Proportion among three quantities)

If 60 women spin 48 kg of cotton by working 8 hours daily, how much cotton will 30 women spin by working 12 hours daily? 

Solution: 

As the number of Women decrease, the cotton spin will also decrease. It is a direct proportion. 

As the working time increase, the cotton spin will also increase. It is also a direct proportion. 

Let the cotton spin be ｘ kg

Here the equation will be 

`\frac{ｘ}{48}`  = `\frac{12}{8}` ｘ `\frac{30}{60}` 

Or

ｘ = `\frac{12}{8}` ｘ `\frac{30}{60}`  ｘ 48 kg

by simplifying we get

ｘ =  36 kg

Thus, 36 kg cotton will be spin