Of the three numbers whose average is $60,$ the first is one-fourth of the sum of the others. The first number is

The average expenditure of a man for the first five months is $Rs.\, 3600$ and for next seven months it is $Rs.\, 3900 .$ If he saves $Rs.\, 8700$ during the $year,$ his average income per $month$ is (in $Rs.$)

There was one mess for $30$ boarders in a certain hostel. On the number of boarders being increased by $10,$ the expenses of the mess were increased by $Rs.\,40$ per month while the average expenditure per head diminished by $Rs.\,2.$ Find out actual monthly expenses. (in $Rs.$)

The average of $6$ numbers is $20 .$ If one number is removed, the average becomes $15 .$ What is the number removed?

A student was asked to find the arithmetic mean of the numbers $3,11,7,9,15,13,8,19,17,21,14$ and $x$. He found the mean to be $12 .$ What should be the number in place of $x ?$

In a competitive examination, the average marks obtained was $45 .$ It was later discovered that there was some error in computerization and the marks of $90$ candidates had to be changed from $80$ to $50$ , and the average came down to $40$ marks. The total number of candidates appeared in the examination is