Total amount of food available initially: 1200 * 28 Soldier-days

After 4 days, the amount of food remaining: 1, 200 * 24 soldier-days worth.

Let N soldiers be remaining after some are transferred to another fort.

1, 200 * 24 = N * 32

N = 900

Hence, 300 soldiers were transferred.

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*Proportional method*

As the number of soldiers decreases, the number of days the food lasts will increases. As the number of soldiers increases, the number of days the food lasts, will decrease. So number N of soldiers is inversely proportional to the number D of days.

So N = K / D, where K = constant of proportionality

when N = 1,200 then D = 24

So K = N D = 1,200 * 24

When D = 32, N = K / D = 1, 200 * 24 / 32 = 900

Hence, there were only 900 soldier after 4 days. So 1200 - 900 = 300 soldiers are transferred.