There were $35$ students in a hostel. If the number of students is increased by $7,$ the expenditure on food increase by $Rs. \,42$ per $day$ while the average expenditure of students is reduced by $Rs.\, 1.$ What was the initial expenditure on food per day? (in $Rs.$)

The average marks in English of a class of $24$ students is $56 .$ If the Marks of three students were misread as $44,45$ and $61$ in lieu of the actual marks $48,59$ and $67$ respectively, then what would be the correct average ?

The mean marks of $10$ boys in a class is $70 \%$, whereas the mean marks of $15$ girls is $60 \%$. The mean marks of all the $25$ students is

Amitabh's average expenditure for the $January$ to $June$ is $Rs.\, 4200$ and he spends $Rs.\, 1200$ in $January$ and $Rs. \,1500$ in $July.$ The average expenditure for the month of $February$ to $July$ is (in $Rs.$)

A team of $8$ persons joins in shooting competition. The be marksman scored $85$ points, the average score for the team would have been $84. $ The number points the team scored was

There are $6$ consecutive odd numbers in increasing order. The difference between the average of the squares of the first $4$ numbers and the last four numbers is $64 .$ If the sum of the squares of the first and the last element (i.e., odd numbers) is $178 ,$ then the average of all the six numbers is