Question 433642
Let F = the number of pounds in the total food supply.
The soldiers will use up the food in 24 days.

(a) Let x = amount of food (in pounds) each soldier eats per day.
   In 24 days, they will eat 24x pounds of food, using up the F pounds of supply.
We have:  24x  =  F *

We reduce each soldier's ration by 20%,
   then each soldier gets only 80% of his normal amount.
That is, each soldier eats 0.80x pounds of food per day.
   And this will last N days.
We have:  N(0.80x)  =  F **

Equate the two statements:  N(0.80x)  =  24x

  Divide by x:  0.80x  =  24

Divide by 0.80:  x  =  30

   Therefore, the food will last 30 days, 6 days longer.


(b) We want the food to last 40 days.

Each soldier will get a fraction of what he usually gets.
   Call that fraction r.
Each soldier gets rx pounds of food per day.
   In 40 days, they will eat: 40rx pounds of food.
In part (a), the total amount of food is 24x.

So we have:  40rx = 24x   ��   r = 24/40 = 3/5  =  60%

Each soldier will get only 60% of his normal ration.

Therefore, each ration is reduced by 40%.