Question 1.

Total number of students is 250, and we are told that, The percentage of girls was at least 44% and at most 60%.

So the number of girls range from, $0.44\left(250\right)\le Girls\le0.6\left(250\right)$

$110\le Girls\le150$

Statement 1: 

If 50% of the boys and 80% of the girls opted for swimming, that means if the total number of Boys is B, Girls is G where B+G=250. 

Swimming is: 0.5B+0.8G

Statement 2: 

If 70%of the boys and 60% of the girls opted for running, that means

Running is 0.7B+0.6G

Total number of enrolments for swimming and running together will be

(0.7B+0.6G)+(0.5B+0.8G)=1.2B+1.4G

Using the overlapping principle, where I represents people who have enrolled only for one activity and II represents number of people who have enrolled for two activities. 

We know that, $I+II=250=B+G$

$I+2II=1.2B+1.4G$

Subtracting the two equations, 

$II=0.2B+0.4G$

$II=0.2\left(B+2G\right)$

Using B+G=250

$II=0.2\left(250+G\right)$

G can at-most be 150 and at least 110. 

So maximum value of II will be $0.2\left(250+150\right)=80$

Minimum value of II will be $0.2\left(250+110\right)=72$