The average weight of $9$ men in a company is increased by $1 \mathrm{kg},$ when one of the man weighing $50 \mathrm{kg}$ is replaced by a new man. What is the weight of the new man?

The average weight of $10$ men is increased by $2 \mathrm{kg}$ when one of the men, who weighs $45 \mathrm{kg},$ is replaced by a new man. Find the weight of the new man.

The average of $20$ observations was found out to be $55,$ but later on it was found that $76$ was misread as $88.$ Find the correct average.

The average cost of $5$ pencils and $4$ pens is $\mathrm{Rs}.18.$ The average cost of $7$ pencils and $8$ pens is $\mathrm{Rs}.24.$ Find the average cost of $12$ pencils and $12$ pens.

The average wage of a labourer for two consecutive weeks was $₹ 80$ per day. During the first $7$ days, his average wage was $₹ 90$ per day and the average wage during the last $8$ days was $₹ 75$ per day. What was his wage on the $7^{\mathrm{th}}$ day (in rupees)?