Average age of $15$ students of a class is $15\, years.$ Out of these the average age of $5$ students is $14 \,years$ and that of the other $9$ students is $16\, years.$ The age of the $15^{th}$ student is (in $years$)

A batsman makes a score of $270$ runs in the $87^{th}$ inning and thus increases his average by a certain number of runs that is a whole number. Find the possible values of the new average.

The average monthly income of $P$ and $Q$ is $Rs.\,5050.$ The average monthly income of $Q$ and $R$ is $Rs.\,6250$ and the average monthly income of $P$ and $R$ is $Rs.\,5200.$ The monthly income of $P$ 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 $Rs.$)

In an examination the average marks was found to be $60.$ The marks of $80$ candidates had to be changed from $95$ to $70$ each and the average came down to $55$ marks. The total number of candidates attended the examination were

The mean of $19$ observations is $4 .$ If one more observation of $24$ is added to the data, the new mean will be