The mean weight of the boys in a class is 52 kg and the mean weight of the girls is 44 kg. The mean weight of the whole class is 49 kg. Find the ratio of the number of boys to the number of girls.

Let there be $b$ boys and $g$ girls. Then $(52b+44g)/(b+g)=49$, so $52b+44g=49b+49g$, that is $3b=5g$ and $b:g=5$ : 3. Check: $5(52)+3(44)=260+132=392$ and 392 ÷ 8 = 49. Each group's share is the OTHER group's distance from 49 — boys get 49 − 44 = 5 and girls get 52 − 49 = 3 — so pairing each group with its own distance gives the reversed 3 : 5. The option 13 : 11 is merely 52 : 44, the ratio of the two means.