The average age of a group of $9$ students is $20\, \text{years}$. When $6$ more students joined the group,the average age falls by $2\, \text{years}$. The average age of the new students is:

The average marks obtained by $150$ students in an examination is $40$. If the average marks of passed students is $60$ and that of the failed students is $20$,what is the number of students who passed the examination?

The average of $20$ numbers is $30$ and that of other $30$ numbers is $50$. What is the average of all the numbers?

The average age of Sachin $(S)$ and Ganguli $(G)$ is $35 \text{ years}$. If Kaif $(K)$ replaces Sachin,the average age becomes $32 \text{ years}$,and if Kaif $(K)$ replaces Ganguli $(G)$,the average age becomes $38 \text{ years}$. If the average age of Dhoni $(D)$ and Irfan $(I)$ is half of the average age of Sachin,Ganguli,and Kaif,then the average age of all the five people is:

The average of two numbers is $62$. If $2$ is added to the smaller number,the ratio between the numbers becomes $1:2$. The smaller number is

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: