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 $kg$).

The average of a non-zero number and its square is $5$ times the number. The number is

The average weight of $8$ persons increases by $2.5\, kg$ when a new person comes in place of one of them weighing $65\, kg$. What is the weight of the new person? (in $kg$)

The average price of $80$ computers in an electronic shop is $Rs. 30,000$. If the highest and lowest price computers are sold out,then the average price of the remaining $78$ computers is $Rs. 29,500$. The cost of the highest price computer is $Rs. 80,000$. The cost of the lowest price computer is (in $Rs.$): (in $,000$)

Average age of $A, B$ and $C$ is $84 \text{ years}$. When $D$ joins them,the average age becomes $80 \text{ years}$. $A$ new person,$E$,whose age is $4 \text{ years}$ more than $D$,replaces $A$ and the average of $B, C, D$ and $E$ becomes $78 \text{ years}$. What is the age of $A$ (in $\text{years}$)?

The average age of Seema,Sapna,Asha,Kavita,and Atrye is $40 \text{ years}$. The average age of Seema and Sapna is $35 \text{ years}$,and the average age of Asha and Kavita is $42 \text{ years}$. What is the age of Atrye?