Sachin Tendulkar has a certain average for $11$ innings. In the $12^{th}$ innings he scores $120$ runs and thereby increases his average by $5$ runs. His new average is

$A$ man covers $\frac{1}{3}$ of his journey by train at $80\, km/h$,the next $\frac{1}{3}$ by bus at $60\, km/h$,and the rest by bicycle at $30\, km/h$. Find the average speed of the man during the whole journey (in $km/h$).

The average of marks obtained by $120$ candidates was $35.$ If the average of marks of passed candidates was $39$ and that of failed candidates was $15,$ the number of candidates who passed the examination is

$A$ man travels by a car to his office at $60 \, km/h$ and returns home along the same route at $20 \, km/h$. Find the average speed of his whole journey (in $km/h$).

$A$ car owner buys petrol at $Rs. 7.50$,$Rs. 8$,and $Rs. 8.50$ per litre for three successive years. What is the approximate average cost per litre of petrol if he spends $Rs. 4000$ each year?

If the average of $m$ numbers is $n^{2}$ and that of $n$ numbers is $m^{2}$,then the average of $(m + n)$ numbers is