The average age of $30$ girls is $13$ years. The average age of the first $18$ girls is $15$ years. Find the average age of the remaining $12$ girls.

The average of marks obtained by $150$ candidates in a certain examination is $50$. If the average marks of passed candidates is $55$ and that of the failed candidates is $25$,what is the number of candidates who passed the examination?

The average weight of $45$ students in a class was calculated as $36 \, kg$. It was later found that the weight of two students in the class was wrongly calculated. The actual weight of one of the boys in the class was $32 \, kg$,but it was calculated as $34 \, kg$,and the weight of another boy in the class was $45 \, kg$,whereas it was calculated as $40 \, kg$. What is the actual average weight of the $45$ students in the class? (in $kg$) (Rounded off to two digits after decimal)

The mean daily profit made by a shopkeeper,in a month of $30$ days,was $Rs. 350$. If the mean profit for the first $15$ days was $Rs. 275$,then the mean profit for the last $15$ days would be (in $Rs.$)

The average speed of a train running at a speed of $30 \, km/h$ during the first $100 \, km$,at $40 \, km/h$ during the second $100 \, km$,and at $50 \, km/h$ during the last $100 \, km$ is nearly (in $km/h$):

$A$ cyclist goes from one place to another and returns by the same route. He pedals his way uniformly with speed $u$ while going and with speed $v$ while returning. The average speed of his journey is