The average age of three boys is $15$ years. If the ratio of their ages is $3:5:7$,what is the age of the oldest boy in years?

The average of marks obtained by $120$ candidates in a certain examination is $35$. If the average marks obtained by passed candidates are $39$ and those of the failed candidates are $15$,then what is the number of candidates who passed the examination?

$A$ man spends on an average $Rs. 269.47$ for the first $7$ months and $Rs. 281.05$ for the next $5$ months. Find out his monthly salary if he saved $Rs. 308.46$ during the year. (in $Rs.$)

The average weight of $6$ persons is increased by $5 \, kg$ when one of them who weighs $40 \, kg$ is replaced by a new man. The weight of the new man is (in $kg$):

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

The average salary per head of all workers of an institution is $Rs. 60$. The average salary per head of $12$ officers is $Rs. 400$. The average salary per head of the rest is $Rs. 56$. Then,the total number of workers in the institution is?