The sum of five numbers is $260$. The average of the first two numbers is $30$ and the average of the last two numbers is $70$. What is the third number?

The average price per $kg$ of rice at $10$ different places was $Rs. 4.85$. After a week,the price per $kg$ was increased by $20$ paise at $3$ places and decreased by $10$ paise at $1$ place. What is the new average price per $kg$ in $Rs.$?

$A$ 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 $x$ and $\frac{1}{x} (x \neq 0)$ is $M$,then the average of $x^{2}$ and $\frac{1}{x^{2}}$ is

$A$ man spends $Rs. 1800$ monthly on an average for the first four months and $Rs. 2000$ monthly for the next eight months and saves $Rs. 5600$ a year. His average monthly income is (in $Rs.$)

There were $35$ students in a hostel. If the number of students is increased by $7$,the expenditure on food increases by $Rs. \,42$ per day,while the average expenditure per student is reduced by $Rs. \,1$. What was the initial total expenditure on food per day? (in $Rs.$)