One or Both

Joseph's solution involved trial and improvement:

First I decided that the number of pupils in the class had to be a mulitple of 10 so that I could work out the percentages with no fractions of people.

I started with 20 pupils in the class. This meant that 14 passed one question (70%) and 12 the other (60%). As 9 pupils passed both questions this meant that 5 got only the first one right (14-9) and 3 the second one, making a total of 9 + 5 + 3 = 17 pupils. This is not enough as I started my working with 20 pupils.

Next I tried 30 pupils in the class. This time 21 passed one question (70% of 30) and 18 passed the other question (60%). Taking out the 9 pupils who passed both gave:
21-9 = 12 passing one question,
18-9 = 9 passing the other
9 passing both.
This makes a total of 30 (12+9+9), which is right

There were 30 pupils in the class.

This is Zi Heng's solution:

70% + 60%	= 130%
130% - 100%	= 30%
30%	= 9 pupils
100%	= 9/30 * 100
	= 30 pupils.

30 pupils took the exam.

Andrei, School 205, Bucharest, Romania solved this problem using a Venn diagram.

Let A be the set of solvers of the first problem, and B the set of solvers of the second problem and the number in set A be written $n(A)$ etc. Their intersection has 9 elements: $$n(A\cap B)=9$$ Their union contains all students. It is evident that: $$n(A\cup B)=n(A)+n(B)-n(A\cap B)$$ If x is the number of students participating in the exam, then A has 70 per cent of x elements, B has 60 per cent of x elements, and relation (2) can be re-written as $x=0.7x+0.6x-9$ or $x=30$. So, 30 pupils came to the exam, 21 solved the first problem and 18 the second one.

Prateek , James , Alan , Jenny and Robert also sent in good solutions. Joseph's solution to the second part of the problem stated: