Explanation

Initial situation: 200 men have enough food for 60 days.

Reduced situation: 160 men (40 fewer men than initially).

Since there are fewer men, the food will last longer. To find out how long, we can set up a proportion:

200 men / 160 men = 60 days / x days

Where x is the number of days the food will last with 160 men.

Cross-multiplying and solving for x:

200x = 60 × 160

200x = 9600

x = 9600 ÷ 200

x = 75

So, the food will last 75 days if the number of men in the camp is reduced to 160.