The average of $13$ results is $60$. If the average of the first $7$ results is $59$ and that of the last $7$ results is $61$,what will be the seventh result?

The mean of $50$ observations was $36$. It was found later that an observation $48$ was wrongly taken as $23$. The corrected new mean is

The average expenditure of a man for the first five months is $Rs.\, 3600$ and for the next seven months it is $Rs.\, 3900$. If he saves $Rs.\, 8700$ during the year,his average income per month is (in $Rs.$)

The average salary of the entire staff in an office is $Rs. 120$ per month. The average salary of officers is $Rs. 460$ and that of non-officers is $Rs. 110$. If the number of officers is $15$,then find the number of non-officers in the office?

The average age of a man and his two twin sons,born on the same day,is $30 \, \text{years}$. The ratio of the ages of the father and one son is $5:2$. What is the father's age in $\text{years}$?

In a coconut grove,$(x+2)$ trees yield $60$ nuts per year,$x$ trees yield $120$ nuts per year,and $(x-2)$ trees yield $180$ nuts per year. If the average yield per year per tree is $100$,find the value of $x$.