Question

A garrison of 1200 men has provisions for 36 days. How many days will the provisions last if 400 more men join the garrison?

Answer 1

Hint: In this question, we need to find the number of men will be there if 400 more are being added to the garrison. Now, using the unitary method we can find the provision provided for each man if they provide 36 days for 1200 men. Then, on multiplying the value obtained from the unitary method with the total number of men in the garrison we get the result.

Complete step by step solution:
UNITARY METHOD:
The unitary method is used to solve a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, given in the question that the provision for 1200 men in 36 days
Let us now find the provision provided for each man
Let us assume that the provision provided for each man as x
\[\begin{align}
  & 1200\to 36 \\
 & 1\to x \\
\end{align}\]
Now, using the cross multiplication this can be further written as
\[\Rightarrow 1200\times x=36\times 1\]
Now, on further rearranging the terms we get,
\[\Rightarrow x=\dfrac{36}{1200}\]
Now, if 400 more men are added to the garrison then the total number of men in the garrison will be
\[\Rightarrow 1200+400\]
Now, on further simplification we get,
\[\Rightarrow 1600\]
Let us now find the provision for these 1600 men
Now, on multiplying the unitary value with 1600 we get the provision provided for them
\[\Rightarrow x\times 1600\]
Now, on substituting the respective value of x we get,
\[\Rightarrow \dfrac{36}{1200}\times 1600\]
Now, on cancelling out the common terms we get,
\[\Rightarrow 12\times 4\]
Now, on further simplification we get,
\[\Rightarrow 48\]
Hence, the provision in the garrison if 400 men are added is 48 days.

Note:
Instead of using the unitary method to find the value of provision for each man and then finding that for 1600 men, we can directly solve this by considering if 36 days are provided for 1200 men then how much it would be for 1600 which on further cross multiplication and simplification gives the result.
It is important to note that here 400 men are being newly added which means the 1200 men who are already present will also be present after adding these 400 men. Because if we consider only 400 men instead of 1600 men then the result we get is incorrect.