Question

a) a garrison has enough food to last for 24 days. How much longer will the food last if each individual ration can be reduced by 20%?

b) By how much will each individual ration have to be reduced if the food is to last 40 days? ​

Answer 1

Answer:

Let the daily consumption of food be x kg, the garrison has 24x kg food.

Assuming at present the ration is 100%, then a reduction of 20% would mean 80%(100-20). So the daily consumption comes down to 0.8x kg

Therefore 24x kg would suffice for 24x / 0.8x = 30 days.

The food will last for 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 individual 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%.

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