a) 1.5 m
b) 2 m
c) 2.5 m
d) 2.8 m

Answer: c
Explanation: Let AB is girls and CD is lamp-post AB = 1.5 which casts her shadow EB

$$\eqalign{ & EB = 4.5\,m,\,BD = 3\,m \cr & {\text{Now in }}\Delta AEB \cr & \tan \theta = \frac{{AB}}{{BE}} = \frac{{1.5}}{{4.5}} = \frac{1}{3} \cr & {\text{and in }}\Delta CED \cr & \tan \theta = \frac{{CD}}{{ED}} \Rightarrow \frac{1}{3} = \frac{h}{{4.5 + 3}} \cr & \Rightarrow \frac{1}{3} = \frac{h}{{7.5}} \cr & \Rightarrow h = \frac{{7.5}}{3} – 2.5\,m \cr & {\text{Height of lamp – post}} = {\text{2}}{\text{.5}}\,m \cr} $$