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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28 days

answer is C.

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Detailed Solution

We have given food supplies for 40 days in a hostel for 50 girls.
We know that the two variables

x and y

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 ∝ 1 y ⇒ x = k 1 y ⇒ x = k y,        where k is proportianality constant ⇒ x y = k .... (1)

In inverse variation, if

q 1, q 2

are the values of

q

corresponding to the values

p 1, p 2

p

respectively, then

p 1 q 1 = p 2 q 2

The days for food supplies will be decreased as the number of girls increases.
So, the given problem is of inverse proportion.
It is given that 50 girls were living in a hostel and 30 more girls checked into the hostel.
Therefore, the total number of girls in the hostel =