The average weight of a group of $20$ boys was calculated to be $89.4 \, kg$ and it was later discovered that one weight was misread as $78 \, kg$ instead of $87 \, kg$. The correct average weight is (in $kg$).

$A$ librarian purchased $50$ storybooks for his library. He realized that he could get $14$ more books by spending $Rs. 76$ more,and the average price per book would be reduced by $Rs. 1$. What was the average price (in $Rs.$) of each book he initially bought?

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.

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 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 average weight of $36$ students is $50 \,kg$. It was found later that the weight of one of the students was misread as $73 \,kg$,whereas his actual weight was $37 \,kg$. Find the correct average (in $kg$).