The average age of $8$ men is increased by $2$ years when $2$ of them,whose ages are $20$ years and $24$ years respectively,are replaced by $2$ women. What is the average age of these two women (in years)?

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 sum of five consecutive integers is $a$ and the sum of the next five consecutive integers is $b$. Then $\frac{(b-a)}{100}$ is equal to

Visitors to a show were charged $Rs. 15$ each on the first day,$Rs. 7.50$ on the second day,$Rs. 2.50$ on the third day,and the total attendance on the three days was in the ratio $2:5:13$ respectively. The average charge per person for the entire three days is (in $Rs.$):

$A$ batsman makes a score of $270$ runs in the $87^{th}$ inning and thus increases his average by a certain number of runs that is a whole number. Find the possible values of the new average.

The average speed of a cyclist who covers the first,second,and third km at $20, 16,$ and $12 \, km/hr$ respectively (in $km/hr$) is: