A family consists of grand parents, parents and three grand children. The average age of the grand parents is $67\, years,$ that of the parents is $35\, years$ and that of the grand children is $6 \,years.$ What is the average age of the family? (in $years$)

Out of $30$ teachers of a school, a teacher of age $60$ $years$ retired. In his place another teacher of age $30$ $years$ was appointed. As a result, the mean age of the teachers will

The mean of $11$ numbers is $35 .$ If the mean of first $6$ numbers is $32$ and that of the last $6$ numbers is $37,$ then find the sixth number.

In an entrance examination, Ritu scored $56$ percent marks, Smita scored $92$ percent marks and Rina scored $634$ marks. The maximum marks of the examination is $875 .$ What is the average marks scored by all the three girls together ?

The mean weight of $34$ students of a school is $42\, kg$. If the weight of the teacher be included, the mean rises by $400\, g.$ Find the weight (in $kg$) of the teacher.