Of three numbers,the second is thrice the first and the third number is three-fourths of the first. If the average of the three numbers is $114$,the largest number is

The average marks of a class of $35$ children is $35$. The marks of one of the students,who got $35$,was incorrectly entered as $65$. What is the correct average of the class?

$A$ man retired from his service at the age of $60$. He served for $\frac{3}{5}$ of his retirement age. At what age (in $years$) did he join his job?

If the average of the ages of Rakesh and Mohan is $15$,the average of the ages of Mohan and Ramesh is $12$,and the average of the ages of Rakesh and Ramesh is $13$,then what is the age of Mohan?

$A$ batsman has a certain average of runs for $12$ innings. In the $13^{th}$ innings,he scores $96$ runs,thereby increasing his average by $5$ runs. What is his average after the $13^{th}$ innings?

The average salary of all the staff in an office of a corporate house is $Rs. 5,000$. The average salary of the officers is $Rs. 14,000$ and that of the rest is $Rs. 4,000$. If the total number of staff is $500$,what is the number of officers?