Of the 60 students in a class, only the students who had obtained Grade A in Science could apply for a scholarship. Only 1 out of every 5 students who applied for a scholarship got it. If the ratio of the number of students who got the scholarship to the number of students who did not get the scholarship is not more than 1:9, what is the maximum possible number of students who applied for but did not get the scholarship? Assume that all the students who were eligible for the scholarship applied for it.

(A) 6

(B) 12

(C) 24

(D) 30

(E) 54

______________________

I like doing things algebraically

. So, I'll try to make some quick equations here.

Total # of students = 60

Let us assume that x students finally got the scholarship. This means that 5x students applied for the scholarship (These are the one's who have got an A grade in Science, smart students

)

This means that there are 4x students who applied BUT did not got the scholarship, and there are some students who in the first place could not get in A in Science.

Let us assume that the # of students who could not apply be y

This means y =60-5x

And the ratio given in the question is

x/(4x+y) <=1/9

We know that x and y are positives (they are students) so we can cross multiply

And finally on solving we can get x <=4

Or 4x <=24

Therefore, maximum possible value of 4x can be 24

Option C