The average marks of $120$ students are $35.$ If the average of passed students was $39$ and failed students was $15,$ then find the number of students who have passed.

The average of three consecutive odd numbers is $12$ more than one-third of the first of these numbers. What is the last of the three numbers?

The arithmetic mean of $100$ observations is $24$. If $6$ is added to each of the observations and then each of them is multiplied by $2.5$,find the new arithmetic mean.

If the average marks of three batches of $55, 60,$ and $45$ students are $50, 55,$ and $60$ respectively,then the average marks of all the students is:

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 age of a group of persons going for a picnic is $16.75 \text{ years}$. $20$ new persons with an average age of $13.25 \text{ years}$ join the group on the spot,due to which the average age of the group becomes $15 \text{ years}$. Find the number of persons initially going for the picnic.