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?

In the first $10$ overs of a cricket game,the run rate was only $3.2$. What should be the run rate in the remaining $40$ overs to reach the target of $282$ runs?

In a match,the average of runs scored by five players is $49$. If the runs scored by four players are $75, 30, 63,$ and $21$ respectively,then how many runs did the fifth player score?

The average weight of $8$ sailors in a boat is increased by $1 \, kg$ if one of them weighing $56 \, kg$ is replaced by a new sailor. The weight of the new sailor is (in $kg$):

Amitabh's average expenditure from $January$ to $June$ is $Rs. 4200$. He spends $Rs. 1200$ in $January$ and $Rs. 1500$ in $July$. What is the average expenditure for the months of $February$ to $July$ (in $Rs.$)?

The average marks obtained by $150$ students in an examination is $40$. If the average marks of passed students is $60$ and that of the failed students is $20$,what is the number of students who passed the examination?