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?​

Answer 1

Answer:

The poor student gets (1/3) of the prize money.

The rich student gets (1/6) of the prize money.

Step-by-step explanation:

Let N be the amount of the prize money.

With respect to the rich student, the prize money gets

divided into a 1:2 ratio.

So the rich student gets 1/3 of N/2 = (1/6)N

and the school gets (2/3) of N/2 = (1/3)N

The opposite is true for the poor student.

So the prize money is divided as follows:

(1/6)N goes to the rich student

(1/3)N+(1/6)N = (3/6)N = (1/2)N goes to the school

(1/3)N goes to the poor student

So the school gets half of the price money.

The poor student gets (1/3) of the prize money.

The rich student gets (1/6) of the prize money.

Hope it helps!!