Problem with fractions part and whole

Question

A businessman instituted an annual award in a city school, with a part of the award given to the school itself to improve its facilities.

It was stated that if a student from a wealthy family were to top the annual examination, the school would receive twice the amount awarded to the student.

On the other hand, if a student from a poor family were to top the annual examination, the student would be awarded twice the amount that the school would receive.

In one year, two students, one rich and one poor, jointly topped the annual examination. What fraction of the award money did the school receive in this case?

(A) $1/2$

(B) $1/3$

(C) $2/7$

(D) $2/9$

I'm having a difficulty in dividing the total amount in different parts.In my attempt I ended up with multiple variables but lesser equations. A help would be appreciated.

Answer 1

The rules of the award if two students are joint top in the exam are not made clear. $\frac{2}{7}$ fits one interpretation of the rules.

But an alternative interpretation would be that the school receives twice as much as the wealthy student plus half as much as the poor student. In this case the schools receives $\frac{1}{2}$ of the award, the poor student receives $\frac{1}{3}$ of the award and the wealthy student receives $\frac{1}{6}$ of the award.

So the question is ambiguous.

Answer 2

Using ratios makes this one manageable. $$R(School:Rich)=2:1$$ $$R(School:Poor)=1:2=2:4$$ Hence $$R(School:Rich:Poor)=2:1:4$$

So school recieves $$\frac{2}{2+1+4}=\frac{2}{7}$$

Answer 3

Let the wealthy kid get an amount '$x$', then the school will get double of the amount as wealthy kid, so schol will receive an amount equal to '$2x$',

Also the poor kid gets double the amount received by school, so he will get an amount equal to '$4x$'

Total amount: $x+2x+4x=7x$

Fraction of amount received by school is = $\frac{2x}{7x}= \frac 27$