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 $Rs.$)

The mean of the marks obtained by $100$ students is $60 .$ If the marks obtained by one of the students was incorrectly calculated as $75$ whereas the actual marks obtained by him were $65,$ what is the correct mean of the marks obtained by the students?

The average weight of $45$ students in a class is $52\, kg.$ Five of them whose average weight is $48 \,kg$ leave the class and other $5\, students$ whose average weight is $54\, kg$ join the class. What is the new average weight (in $kg$ ) of the class 

Average rainfall on Monday, Tuesday, Wednesday and Thursday is $420.5\, cm$ and average on Tuesday, Wednesday, Thursday and Friday is $440.5\, cm .$ If the ratio of rainfall for Monday and Friday is $20: 21,$ find the rainfall in $cm$ on Monday and Friday.

Of the three numbers, the first is twice the second and the second is thrice the third. If the average of the three numbers is $10,$ the numbers are

If the average marks of three batches of $55,60$ and $45$ students respectively is $50,55$ and $60 ,$ then the average marks of all the students is