The average of $13$ results is $50$. If the average of the first $7$ results is $52$ and that of the last $7$ results is $49$,find the $7^{th}$ result.

The average of the first $n$ consecutive even numbers is $101$. Find their sum.

The average monthly salary of $20$ employees in an organisation is $Rs. 1500$. If the manager's salary is added, then the average salary increases by $Rs. 100$. What is the manager's monthly salary (in $Rs.$)?

The average monthly expenditure of a family for the first four months is $Rs.\, 2570$,for the next three months $Rs.\, 2490$ and for the last five months $Rs.\, 3030$. If the family saves $Rs.\, 5320$ during the whole year,the average monthly income of the family during the year is (in $Rs.$)

The average monthly expenditure of a family for the first four months is $Rs. 2750$,for the next three months is $Rs. 2940$,and for the last five months is $Rs. 3130$. If the family saves $Rs. 5330$ throughout the year,find the average monthly income of the family for that year (in $Rs.$).

The average of marks obtained by $120$ candidates was $35.$ If the average of marks of passed candidates was $39$ and that of failed candidates was $15,$ the number of candidates who passed the examination is