The average of $11$ numbers is $10.9.$ If the average of the first $6$ numbers is $10.5$ and that of the last six digits is $11.4,$ then the middle number is _____.

The average monthly expenditure of a family was $\mathrm{Rs}.2,200$ during the first $3$ months; $\mathrm{Rs}. 2,250$ during the next $4$ months; and $\mathrm{Rs}.3,120$ during the last $5$ months of a year. If the total savings during the year was $\mathrm{Rs}.1260$ then the average monthly income was _____.

A school has $4$ sections of Chemistry in class $10\mathrm{th}$ having $40, 35, 45$ and $42$ students, respectively. The mean marks obtained in Chemistry test are $50, 60, 55$ and $45$ respectively for the $4$ sections. Determine the overall averages of marks per student.

Kapil scored an average of $45$ runs in the first $6$ tests. If the first test is not counted and the seventh is counted, then his average score goes up to $50.$ If the score in the first test was $50$ runs, find his score in the seventh test.