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Hint: In the above given question, keep in mind that the number of soldiers is only added to the existing number of soldiers and is not replaced. Also, try to formulate an equation with the given data so that the unknown values can be easily obtained.

It is given in the question that the food is enough for $60$ days for $800$ soldiers, that means that the food is constant such that

$s \times d = k$ … (1)

Where,

$s = $number of soldiers

$d = $number of days

$k = $constant

That is

After substituting the values in the equation (1), we get

$800 \times 60 = k$ … (2)

Now, according to the question$400$more soldiers have arrived, so the total number of soldiers is raised to $800 + 400 = 1200$

Now, let us assume the number of days for which the food will last for $1200$ soldiers be denoted as $x$.

Therefore, by using the equation (1) again, we get

$1200 \times x = k$ … (3)

After equating equation (2) and (3), we get

$ \Rightarrow 1200 \times x = 800 \times 60$

$ \Rightarrow 1200x = 48000$

$ \Rightarrow x = \dfrac{{48000}}{{1200}}$

$\therefore x = 40$

So, the number of days the food will last for $1200$ soldiers is $40$days.

Note: Whenever we face such types of problems, observe that the quantity of food is constant and we know that, if in a product one quantity is increased, the other has to be decreased. So, here if the number of soldiers increases, the number of days the food will last decreases and vice versa.

It is given in the question that the food is enough for $60$ days for $800$ soldiers, that means that the food is constant such that

$s \times d = k$ … (1)

Where,

$s = $number of soldiers

$d = $number of days

$k = $constant

That is

After substituting the values in the equation (1), we get

$800 \times 60 = k$ … (2)

Now, according to the question$400$more soldiers have arrived, so the total number of soldiers is raised to $800 + 400 = 1200$

Now, let us assume the number of days for which the food will last for $1200$ soldiers be denoted as $x$.

Therefore, by using the equation (1) again, we get

$1200 \times x = k$ … (3)

After equating equation (2) and (3), we get

$ \Rightarrow 1200 \times x = 800 \times 60$

$ \Rightarrow 1200x = 48000$

$ \Rightarrow x = \dfrac{{48000}}{{1200}}$

$\therefore x = 40$

So, the number of days the food will last for $1200$ soldiers is $40$days.

Note: Whenever we face such types of problems, observe that the quantity of food is constant and we know that, if in a product one quantity is increased, the other has to be decreased. So, here if the number of soldiers increases, the number of days the food will last decreases and vice versa.

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