The average of a set of $6$ numbers is $45$. If one number is removed from the set, the average becomes $43$. Which number is removed?

In three numbers, the first is twice the second and thrice the third. If the average of these three numbers is $44,$ then the first number is _____.

The average of $10$ numbers is $40.2.$ Two numbers $13$ and $18$ are removed and $31$ is added instead. Find the new average.

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.