The average expenditure of a man for the first five months is $Rs.\, 3600$ and for the 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 weight of $34$ students of a school is $42\, kg$. If the weight of the teacher is included, the mean weight increases by $400\, g$. Find the weight (in $kg$) of the teacher.

Of the three numbers,the average of the first and the second is greater than the average of the second and the third by $15$. What is the difference between the first and the third of the three numbers?

The average marks obtained by $180$ students in an examination is $50$. If the average marks of passed students is $80$ and the average marks of failed students is $40$,then what is the number of students who failed the examination?

The batting average of a cricket player for $64$ innings is $62$ runs. His highest score exceeds his lowest score by $180$ runs. Excluding these two innings,the average of the remaining innings becomes $60$ runs. His highest score was (in $Runs$):

Three years ago,the average age of a family of $5$ members was $27 \text{ years}$. After the addition of a child to the family,the present average age of the family is still $27 \text{ years}$. Find the present age of the child (in years).