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 $km/h$):

The arithmetic mean of the following numbers is $1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7$.

The average weight of all the $11$ players of the Indian cricket team is $50 \, kg$. If the average weight of the first six lightest players is $49 \, kg$ and that of the six heaviest players is $52 \, kg$,find the weight of the player who is in the sixth position when all $11$ players are arranged in order of increasing weights (in $kg$).

Of three numbers,the second is thrice the first and the third number is three-fourths of the first. If the average of the three numbers is $114$,the largest number is

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

The average monthly income of $P$ and $Q$ is $Rs. 5050$. The average monthly income of $Q$ and $R$ is $Rs. 6250$ and the average monthly income of $P$ and $R$ is $Rs. 5200$. The monthly income of $P$ is