The average age of all the students of a class is 18 years. The average age of the boys of the class is 19 years and of the girls is 14 years. If the number of girls in the class is 30, then what is the number of boys in the class?

Let the number of boys in the class be B.
The number of girls (G) is given as 30.

Using the formula for weighted average:

Average Age=
B+G
(Average of Boys×B)+(Average of Girls×G)
​

18=
B+30
19B+14×30
​

18(B+30)=19B+420
18B+540=19B+420
540−420=19B−18B
B=120
Alternatively, using the rule of alligation:

Boys' Avg Girls' Avg
19 14
\ /
18
/ \
(18-14) (19-18)
= 4 = 1
Ratio of Boys : Girls = 4:1

Since the number of girls represents 1 part = 30,
The number of boys represents 4 parts = 4×30=120.