The arithmetic mean of the scores of a group of students in a test was $52$. The brightest $20\%$ of them secured a mean score of $80$ and the dullest $25\%$ a mean score of $31$. The mean score of the remaining $55\%$ is

The average weight of $15$ oarsmen in a boat is increased by $1.6\, kg$ when one of the crew,who weighs $42\, kg$,is replaced by a new man. Find the weight of the new man (in $kg$).

$A$ batsman in his $17^{th}$ innings makes a score of $85$ runs,and thereby,increases his average by $3$ runs. What is his average after the $17^{th}$ innings? He had never been 'not out'.

The average age of $24$ boys and their teacher is $15 \text{ years}$. When the teacher's age is excluded,the average age decreases by $1 \text{ year}$. What is the age of the teacher in years?

The average weight of $4$ men $A, B, C,$ and $D$ is $67 \, kg.$ When a $5^{th}$ man $E$ is included,the average weight decreases by $2 \, kg.$ $A$ is replaced by $F.$ The weight of $F$ is $4 \, kg$ more than $E.$ The average weight decreases because of the replacement of $A,$ and now the average weight is $64 \, kg.$ Find the weight of $A.$

The average of $X_{1}, X_{2}$ and $X_{3}$ is $14$. Twice the sum of $X_{2}$ and $X_{3}$ is $30$. What is the value of $X_{1}$?