The average of first three numbers is double of the fourth number. If the average of all the four numbers is $12,$ find the $4^{th}$ number.

The average weight of $24$ students is $35\, kg$. If the weight of the teacher is added, the average increases by $400\, g$. What is the weight of the teacher in $kg$?

$10 \, kg$ of rice priced at $Rs. \, 12$ per $kg$ is mixed with $6 \, kg$ of rice priced at $Rs. \, 16$ per $kg$. Find the average price in $Rs.$ per $kg$ of the whole mixture?

$A, B, C$ and $D$ are four consecutive even numbers,respectively,and their average is $65$. What is the product of $A$ and $D$?

Five years ago,the average age of a husband and wife was $23 \text{ years}$. Today,the average age of the husband,wife,and child is $20 \text{ years}$. How old is the child in years?

The average of $5$ consecutive integers starting with $m$ is $n$. What is the average of $6$ consecutive integers starting with $(m+2)?$