There are food supplies for 40 days in a hostel for 50 girls. How long will these supplies last if 30 more girls check into the hostel?

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20 days

22 days

25 days

28 days

answer is C.

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Detailed Solution

We have been given food supplies for 40 days in a hostel for 50 girls.
We have to find how long the same food supply will last if we have 30 more girls.
We know that two variables are said to be inversely proportional if and only if they are directly proportional to one another's reciprocal. If

x and y

are two variables in inverse variations, then

x y = k,

where k is a proportionality constant.
The days for food supplies will be decreased as the number of girls increases.
So, the given problem is of inverse proportion.
Let us make a table as shown below:

Number of girls

$(x)$

Number of days

$y$

$x 1 = 50$

$y 1 = 40$

$x 2 = 50 + 30 = 80$

$y 2 =$ ?

Using the relation of inverse proportion