Three years ago,the average age of a family of $5$ members was $27 \, \text{years}$. The present average age is also $27 \, \text{years}$ after the inclusion of a child into the family. Find the age of the child in years.

The mean of the marks obtained by $100$ students is $60$. If the marks obtained by one of the students was incorrectly calculated as $75$ whereas the actual marks obtained by him were $65$,what is the correct mean of the marks obtained by the students?

The average value of the numbers $15, 21, 32, 35, 46, x, 59, 65, 72$ should be greater than or equal to $43$ but less than or equal to $44$. Then the value of $x$ should be

The average of three consecutive odd numbers is $52$ more than $\frac{1}{3}$ of the largest of these numbers. What is the smallest of these numbers?

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 $x$.

The average annual income (in $Rs.$) of certain agricultural workers is $S$ and that of other workers is $T$. The number of agricultural workers is $11$ times that of other workers. Then the average annual income (in $Rs.$) of all the workers is