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A businessman instituted an annual award in a city school, with 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 ?

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  • $\begingroup$ 1/2 but I am not sure I understood the question. $\endgroup$
    – isaace
    Commented Apr 19, 2018 at 17:14
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    $\begingroup$ This is a question from an examination held in India and the wordings are as such. Even I thought the answer to be 1/2 but that's not the case $\endgroup$
    – Ashish Panigrahi
    Commented Apr 19, 2018 at 17:16
  • $\begingroup$ This seems like a blatent math problem. This does not beling in Puzzling SE, and will be flagged as off-topic $\endgroup$
    – Prince North Læraðr
    Commented Apr 19, 2018 at 19:46

3 Answers 3

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Let's work this out in pieces.

The trick is that

You have to realize that the amounts the two kids get aren't directly based on each other, they're based on what the school gets.

So say that, at the end of the day, after all the math nonsense, the school gets some amount of money s. We know that

The wealthy kid will get half of that amount, or 0.5s

and

The poor kid will get double that amount, or 2s.

So the total amount of money T would be

s + 0.5s + 2s = 3.5s = T

And the school gets

1 out of 3.5 pieces, or 1 / 3.5 (or 2/7 to avoid decimals in the fraction).

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Rich student gets \$1.

School gets twice what rich student gets = \$2.

Poor student gets twice what the school gets = \$4.

School gets 2/7

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  • $\begingroup$ What the heck? The spoiler tags are acting weird $\endgroup$
    – Prince North Læraðr
    Commented Apr 19, 2018 at 19:50
  • $\begingroup$ Hmm. I'm sorry, but I had to get rid of the $. It was causing weird problem — would cause the text to go into a weird cursive font. $\endgroup$
    – Prince North Læraðr
    Commented Apr 19, 2018 at 19:56
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Contrary to the accepted answer, it seems fair to me that each student should receive the same sum of money S.

That means that the school receives:

2 * S + 1/2 * S = 5/2 * S

Let T be the total sum of money awarded:

T = S + S + 5/2 S = 9/2 S

The school would then receive the following fraction of the total:

r = (5/2 * S) / (9/2 * S) = 5/9

For example:

If the total sum awarded is 90 euros, then:
- Each student gets 20 euros
- The school gets 2 * 20 + 20 / 2 = 50 euros = 5/9 * 90

As a side note, giving more money to a school when a rich gets rewarded is a weird incentive IMHO. Maybe I'm missing something but having a poor student rewarded seems more difficult than having a rich one awarded.

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