There are 714 boys in that school, you can cross multiply and divide to find the answer, if you wanna check. The way I wrote it was x (boys) / 1309 = 6/11.
We have the expression

We can already simplify x because it's both on the numerator and denominator

Now we can simplify 425/25 = 17

Remember that

Then

The final result is
All you need to do is add te averages together then divide them by 2.
91%+78%=169%
169%÷2=84.5%
So the new test average is 84.5%