The average age of $30$ women decreases by $3$ months if a new person,Neha,is included in place of a $25$ year old woman. Calculate the age of Neha in years.

An aeroplane travels $2500 \, km$,$1200 \, km$,and $500 \, km$ at $500 \, km/h$,$400 \, km/h$,and $250 \, km/h$ respectively. The average speed is (in $km/h$):

The average of $6$ numbers is $8$. What is the $7^{th}$ number so that the average becomes $10$?

The average age of $x$ and $y$ is $20$ years. If $z$ were to replace $x$,the average would be $19$ and if $z$ were to replace $y$,the average would be $21$. Find the ages of $x, y$ and $z$.

There were $35$ students in a hostel. If the number of students increases by $7$,the expenses of the mess increase by $Rs. 42$ per day while the average expenditure per head decreases by $Rs. 1$. Find the original expenditure of the mess in $Rs$.

The average speed of a cyclist who covers the first,second,and third km at $20, 16,$ and $12 \, km/hr$ respectively (in $km/hr$) is: