The average of two numbers is $62$. If $2$ is added to the smaller number,the ratio between the numbers becomes $1:2$. The smaller number is

The average age of $5$ members is $21 \text{ years}$. If the age of the youngest member is $5 \text{ years}$,find out the average age of the family at the birth of the youngest member (in $\text{years}$).

The average of $5$ consecutive integers starting with $m$ is $n$. What is the average of $6$ consecutive integers starting with $(m + 2)$?

There were $35$ students in a hostel. If the number of students is increased by $7$,the expenditure on food increases by $Rs. \,42$ per day,while the average expenditure per student is reduced by $Rs. \,1$. What was the initial total expenditure on food per day? (in $Rs.$)

The average age of $30$ women decreases by $3$ months if a new person,Neha,is included in place of a $25$ year old woman. Calculate the age of Neha in years.

The average of marks obtained by $100$ candidates in a certain examination is $30$. If the average marks of passed candidates is $35$ and that of the failed candidates is $10$,what is the number of candidates who passed the examination?