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Answer: 7
Using expressions
Let the number of Boys in Group 1 be $x$.
The number of Girls in Group 1 is therefore $40-x$.
Therefore the number of Girls in Group 2 is $33 - (40 - x) = x - 7$.
There are therefore $7$ more Boys in Group 1 than Girls in Group 2.
Using an example
If all the Boys are in Group 1 there will be:
If we swap one Boy from Group 1 with one Girl from Group 2 there will be:
If we continue in the same way, as the number of Boys in Group 1 goes down by 1, the number of Girls in Group 2 will also go down by 1, so the difference will always be 7.
Using a table
$$\begin{align}30-b&=37-a\\
-b+a&=37-30\\
a-b&=7\end{align}$$
Forming Groups
Age 11 to 14
ShortChallenge Level 
Answer: 7
Using expressions
Let the number of Boys in Group 1 be $x$.
The number of Girls in Group 1 is therefore $40-x$.
Therefore the number of Girls in Group 2 is $33 - (40 - x) = x - 7$.
There are therefore $7$ more Boys in Group 1 than Girls in Group 2.
Using an example
If all the Boys are in Group 1 there will be:
37 Boys and 3 Girls in Group 1
30 Girls in Group 2
If we swap one Boy from Group 1 with one Girl from Group 2 there will be:
36 Boys and 4 Girls in Group 1
29 Girls and 1 Boy in Group 2
29 Girls and 1 Boy in Group 2
If we continue in the same way, as the number of Boys in Group 1 goes down by 1, the number of Girls in Group 2 will also go down by 1, so the difference will always be 7.
Using a table
$$\begin{align}30-b&=37-a\\
-b+a&=37-30\\
a-b&=7\end{align}$$
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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