1440 men had sufficient food for 32 days in a camp. How many men may leave the camp so that the same food is sufficient for 40 days when the ration is increased by 1`\frac{1}{2}` times? [Hint: The 1st element (food) is 1 and the 2nd element (food) is `\frac{3}{2}` ]

Solution:  

Given: 
Let the food is = 1
The food increased = 1`\frac{1}{2}` = `\frac{3}{2}`
increase food  = 1 + `\frac{3}{2}` = `\frac{5}{2}`

Now
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 


Here the equation will be 

`\frac{ｘ}{1,440}`  = `\frac{1}{frac{5}{2}` ｘ `\frac{32}{42}` 

Or

ｘ = `\frac{2}{5}` ï½˜ `\frac{32}{42}`    ï½˜ 1440 men

by simplifying we get

ｘ =  768 Men

Thus, the same food will be sufficient for 2400 men. So, 1,440 - 768 = 672 may leave.