The other tutor did not get the smallest total. It's 22, not 24. 

If the 6 kids were as young as possible with all different ages,
with the youngest being 1, the kids' ages would be 1 through 6,
1+2+3+4+5+6 = 21.  But 3 of them must have the same sum as the 
other 3, since the sum of the girls' ages equals the sum of the 
boys' ages.  So the sum of all 6 must be an even number, so we 
can split it in half. So we must change the 6 to 7, so the ages 
are 1,2,3,4,5,7, which has even sum 22.  That means the sum of 
the boys' ages and the sum of the girls' ages are 11 each.  For 
instance, the boys could have ages 1,3,7 and the girls have ages 
2,4,6.

So the smallest possible total of the 6 ages is 22.

Edwin