The mean daily profit made by a shopkeeper, in a month of $30\, days,$ was $Rs.\,350.$ If the mean profit for the first $15\, days$ was $Rs.\, 275,$ then the mean profit for the last $15\, days$ would be (in $Rs\,$)

The average of the test scores of a class of $'m'$ students is $70$ and that of $'n'$ students is $91.$ When the scores of both the classes are combined, the average is $80 .$ What is $n / m$ ?

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

$10$ years ago, the average age of a family of $4$ members was $24$ $years.$ Two children having been born (with age difference of $2\, years$), the present average age of the family is the same. The present age of the youngest child is (in $years$)

The average of marks obtained by $120$ candidates was $35.$ If the average of marks of passed candidates was $39$ and that of failed candidates was $15,$ the number of candidates who passed the examination is

What is the average of the squares of the first $19$ natural numbers ?