Out of four numbers,whose average is $60$,the first one is one-fourth of the sum of the last three. The first number is

Of the three numbers,the average of the first and the second is greater than the average of the second and the third by $15$. What is the difference between the first and the third of the three numbers?

If the average of the ages of Rakesh and Mohan is $15$,the average of the ages of Mohan and Ramesh is $12$,and the average of the ages of Rakesh and Ramesh is $13$,then what is the age of Mohan?

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:

The average of six numbers is $32$. If each of the first three numbers is increased by $2$ and each of the remaining three numbers is decreased by $4$,then the new average is?

The mean of the marks obtained by $100$ students is $60$. If the marks obtained by one of the students was incorrectly calculated as $75$ whereas the actual marks obtained by him were $65$,what is the correct mean of the marks obtained by the students?