A and B are in the ratio 2:5.
A=2k and B=5k for some value k.
B and C are in the ratio 1:9.
B=m and C=9m for some value m.
Since both expressions represent B:
5k=m
C=9m
C=9(5k)
C=45k
All three numbers in terms of k:
A=2k
B=5k
C=45k
The sum equals 156:
A+B+C=156
2k+5k+45k=156
52k=156
k=3
B=5k
B=5×3
B=15