If 4200 men have sufficient food for 32 days at a rate of 12 hectogram per person, how many men may leave so that the same food be sufficient for 42 days at a rate of 16 hectogram per person? 

Solution:  
As the number of days increase, the number of men decreases. So,it is an Inverse Proportion.
As the quantity of food increases the number of men decreases. So it is also Inverse Proportion. 

Let the number of men be X then the vertical form



Here the equation will be 

`\frac{ｘ}{4,200}`  = `\frac{16}{12}` ï½˜ `\frac{32}{42}` 

Or

ｘ = `\frac{16}{12}` ï½˜ `\frac{32}{42}`    ï½˜ 4,200 men

by simplifying we get

ｘ =  2,400 Men

Thus, the same food will be sufficient for 2400 men. So, 4,200 - 2,400 = 1,800 may leave.