In an army camp, there are $800$ soldiers. There is enough food for them for $60$ days. If $400$ more soldiers arrive at the camp, how many days will the food last?
Last updated date: 26th Mar 2023
•
Total views: 309k
•
Views today: 4.85k
Answer
309k+ views
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.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India
