The bar shows the total number of students in four schools and it also shows the difference between boys and girls in these schools.

If boys in D increase by 25% and girls decreased by 50%, then find the new number of total students in D.

Based on the provided bar chart, we can extract the values for School D:
Total number of students (Boys + Girls) in School D = 52
Difference between boys and girls (Boys - Girls) in School D = 4

Let the number of boys in School D be $B$ and the number of girls be $G$. We can set up the following two linear equations:

1) $B+G=52$

2) $B-G=4$

To find the number of boys ($B$), we add equations (1) and (2):
$(B+G)+(B-G)=52+4$
$2B=56$
$B=28$

To find the number of girls ($G$), we substitute $B=28$ back into equation (1):
$28+G=52$
$G=52-28=24$

Now, we calculate the changes in the student population for School D:
The number of boys increases by 25%:
$\text{New Boys}=28+(25\%\text{of}28)=28+(0.25\times 28)=28+7=35$

The number of girls decreases by 50%:
$\text{New Girls}=24-(50\%\text{of}24)=24-(0.50\times 24)=24-12=12$

Finally, we find the new total number of students in School D:
$\text{New Total Students}=\text{New Boys}+\text{New Girls}=35+12=47$

Therefore, the correct option is 47.