Let every soldier require "x" units of food every day. I am using "x" in bold to distinguish it from the multiplication sign.

So, 1600 soldiers will need 1600x units of food every day. So, 1600 soldiers will require 1600x × 60 units of food for 60 days; this is the total food provision, which the soldiers carried to sustain them for 60 days.

For the first 15 days, all the 1600 soldiers ate from this provision. Now, 1600 soldiers need 1600x units of food every day; so, they will need 1600x × 15 units of food for 15 days. At the end of 15 days, this amount of food was eaten up.

So, the amount of provisions remaining after 15 days = 1600x × 60 - 1600x × 15 = 1600x × 45.

At the end of the 15th day, 600 soldiers leave. So, all this 1600x × 45 units of food will be available to the rest of the 1000 soldiers.

One soldier needs "x" units of food every day, so 1000 soldiers will need 1000x units of food every day. Now, 1000x units of food last for one day, so, 1600x × 45 units of food will last for 1600x × 45 / 1000x days = 1.6 × 45 = 72 days.

I hope I have done it right. Do you think the answer is correct?

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