The average of five numbers is $27$. If one number is excluded,the average becomes $25$. The excluded number is

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 of $13$ results is $50$. If the average of the first $7$ results is $52$ and that of the last $7$ results is $49$,find the $7^{th}$ result.

The average of $11$ numbers is $10.9$. If the average of the first six is $10.5$ and the average of the last six is $11.4$, find the middle (sixth) number.

If the average of the ages of Rakesh and Mohan is $15$,the average of the ages of Mohan and Ramesh is $12$,and the average of the ages of Rakesh and Ramesh is $13$,then what is the age of Mohan?

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 $kg$).