The average of marks obtained by $100$ candidates in a certain examination is $30$. If the average marks of passed candidates is $35$ and that of the failed candidates is $10$,what is the number of candidates who passed the examination?

Visitors to a show were charged $Rs. 15.00$ each on the first day,$Rs. 7.50$ on the second,and $Rs. 2.50$ on the third day. The total attendance of visitors for the three days was in the ratio $2:5:13$. Find the average charge per visitor for the entire show (in $Rs.$).

On $24^{\text{th}}$ May,$2008$,the maximum temperatures of Delhi,Kolkata,and Mumbai were recorded as $35^{\circ}C$,$33^{\circ}C$,and $34^{\circ}C$ respectively. What was the maximum temperature of Chennai so that the average maximum temperature of those four cities would be $35^{\circ}C$ (in $^{\circ}C$)?

$A$ batsman makes a score of $81$ runs in the $16^{\text{th}}$ match and thus increases his average runs per match by $3$. What is his average after the $16^{\text{th}}$ match?

The average age of $30$ girls is $13$ years. The average age of the first $18$ girls is $15$ years. Find the average age of the remaining $12$ girls.

The average age of $8$ men is increased by $2$ years when $2$ of them,whose ages are $20$ years and $24$ years respectively,are replaced by $2$ women. What is the average age of these two women (in years)?