The average age of a family of $6$ members $4$ years ago was $25$ years. Meanwhile,a child was born in this family,and the average age of the whole family is still the same today. The present age of the child in years is?

$30$ pens and $75$ pencils altogether were purchased for $Rs. \, 510$. If the average price of $75$ pencils was $Rs. \, 2$,then what was the average price of a pen? (in $Rs.$)

The average age of $5$ sisters is $20 \, \text{years}$. If the age of the youngest sister is $4 \, \text{years}$,what was the average age of the group of sisters at the time of the birth of the youngest sister?

The average of $X_{1}, X_{2}$ and $X_{3}$ is $14$. Twice the sum of $X_{2}$ and $X_{3}$ is $30$. What is the value of $X_{1}$?

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

$A$ 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 $Rs.$)