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?

$30$ pens and $75$ pencils altogether were purchased for $Rs. \, 510$. If the average price of $75$ pencils was $Rs. \, 2$,then what was the average price of a pen? (in $Rs.$)

In a set of prime and composite numbers,the number of composite numbers is twice the number of prime numbers,and the average of all the numbers in the set is $9$. If the number of prime numbers and composite numbers are exchanged,then the average of the set of numbers increases by $2$. If,during the exchange of the numbers,the average of the prime numbers and composite numbers individually remained constant,then what was the ratio of the average of composite numbers to the average of prime numbers (initially)?

The average age of $20$ boys in the class is $15.6$ years. Five new boys join and the new average becomes $15.56$ years. What is the average age of the five new boys (in years)?

The mean daily profit made by a shopkeeper,in a month of $30$ days,was $Rs. 350$. If the mean profit for the first $15$ days was $Rs. 275$,then the mean profit for the last $15$ days would be (in $Rs.$)

The average salary of all the workers in a workshop is $Rs. 8000$. The average salary of $7$ technicians is $Rs. 12000$ and the average salary of the rest is $Rs. 6000$. The total number of workers in the workshop is