Discover the Lower Quartile Math Definition and Examples

Can anyone help me with statistics?
Question: Following is the distribution of marks obtained by 500 candidates in the statistics paper of a civil services examination:
+ marks more than: 0 10 20 30 40 50
+ number of candidates: 500 460 400 200 100 30
Calculate the lower quartile marks. If $70\mathrm{\%<!--\; \%\; -->}$ of the candidates pass in the paper, find the minimum marks obtained by a passing candidate.
In the above problem, I am able to find the first part to calculate lower quartile marks but not able to find the second section.
Anyone, please help I am a newbie to statistics.
Thanks in advance, please ignore the bad English.

$\mathrm{\mu <!--\; \mu \; -->}=m=\frac{q_1+q_3}{2}$
Let $X$ be a random variable with p.m.f./p.d.f. $f_X(x)$ that is symmetric about $\mathrm{\mu <!--\; \mu \; -->}(\in <!--\; \in \; -->R),$ i.e., $f_X(x+\mathrm{\mu <!--\; \mu \; -->})=f_X(\mathrm{\mu <!--\; \mu \; -->}-x)$, $\mathrm{\forall <!--\; \forall \; -->}x\in <!--\; \in \; -->(-\mathrm{\infty <!--\; \infty \; -->},\mathrm{\infty <!--\; \infty \; -->}).$
If $q_1,m$ and $q_3$ are respectively the lower quartile, the median and the upper quartile of the distribution of $X$ then show that $\mathrm{\mu <!--\; \mu \; -->}=m=\frac{q_1+q_3}{2}$
How to prove.....
any Hints.

What is the meaning of percentile?
I am confused by the term percentile. Once my teacher told me that percentile means the percentage with respect to the score of the highest achiever.
This means that if in a competition I got $80$ out of $100$ and the highest score in that competition was 90 out of 100 then my percentile would be $\frac{80}{90}\ast <!--\; \ast \; -->100=88.89$
So I got $80\mathrm{\%<!--\; \%\; -->}$ and $88.89$ percentile.
I was believing that my above concept was right.
But when I see the definition of percentile on Wikipedia then I got something new (but I don't understand this definition) and then I thought that what my teacher told me was wrong.
Kindly tell me if my teacher right or wrong.