Word Problem No.7 (Compound Proportion) --- Masons, Wall Height, and Days (Compound Proportion among three quantities)

14 masons can build a wall 12 metres high in 12 days. How many masons will be needed to build a wall 120 metres high in 7 days? 

Solution: 

As the Height of wall increase, the more masons will be needed. so, It is a direct proportion. 

As the working days decrease, the more masons will be needed. It is a Inverse proportion. 

Let the numbers of masons be ｘ then,

Here the equation will be 

`\frac{ｘ}{14}`  = `\frac{120}{12}` ｘ `\frac{12}{7}` 

Or

ｘ = `\frac{120}{12}` ｘ `\frac{12}{7}`    ｘ 14 Masons

by simplifying we get

ｘ =  240 Masons

Thus, 240 Masons will be needed to construct the required wall.