If the mean of $a, b, c$ is $M$ and $a b+b c+c a=0,$ then the mean of $a^{2}, b^{2}, c^{2}$ is

Nine friends have a dinner in a hotel. Eight of them spent $Rs.\, 12$ each on their meals and the ninth spent $Rs. \,16$ more than the average expenditure of all the nine. Find out the total money in $Rs.$ spent by them?

The average marks of a class of $35$ children is $35 .$ The marks of one of the students, who got $35,$ was incorrectly entered as $65 .$ What is the correct average of the class?

The arithmetie mean of the scores of a group of students in a test was $52 .$ The brightest $20 \%$ of them secured a mean score of $80$ and the dullest $25 \%$ a mean score of $31.$ The mean score of remaining $55 \%$ is

The average age of a husband and wife, who were married $7 \,years$ ago, was $25\, years$ at the time of their marriage, Now, the average age of the family, including husband, wife and a child, born during the interval, is $22\, years.$ What is the present age of the child in $year$ ?

The average of first three numbers is double of the fourth number. If the average of all the four numbers is $12,$ find the $4^{th}$ number.