The average of certain first consecutive natural numbers is $20.5$. Find their sum.

The average temperature from Monday to Thursday is $48^{\circ}C$ and from Tuesday to Friday is $52^{\circ}C$. If the temperature on Monday is $42^{\circ}C$,what was it on Friday? (in $^{\circ}C$)

The average age of a group of $15$ students is $10 \, \text{years}$. When $5$ more students joined the group,the average age increased by $1 \, \text{year}$. If the average age of the $5$ new students is $x$,find the value of $x$ (in $\text{years}$).

The mean of $50$ observations was $36$. It was found later that an observation $48$ was wrongly taken as $23$. The corrected new mean is

The average of marks obtained by $120$ candidates in a certain examination is $35$. If the average marks obtained by passed candidates are $39$ and those of the failed candidates are $15$,then what is the number of candidates who passed the examination?

The mean weight of $34$ students of a school is $42\, kg$. If the weight of the teacher is included, the mean weight increases by $400\, g$. Find the weight (in $kg$) of the teacher.