Word Problem No.13 (Compound Proportion) -- Labourers, Time, digging Erath (Proportion between three quantities)

If 35 labourers dig 805 cm³ of earth in 5 hours, how much of the earth will 30 labourers dig in 6 hours? 

Solution: 

According to given conditions, As the number of labourers decrease, the earth dug will also decrease. It is a direct proportion. 

As the working time increase, the earth dug will also increase. It is also a direct proportion. Let the earth dug be ｘ cm³

Here the equation will be 

`\frac{ｘ}{805}`  = `\frac{6}{5}` ｘ `\frac{30}{35}` 

Or

ｘ = `\frac{6}{5}` ｘ `\frac{30}{35}` ｘ 805 cm³

by simplifying we get

ｘ =  828 cm³

Thus, 828 cm³ earth will be dug