A man standing south of lamp post, observes his shadow on the horizontal to be 24 meters long, on walking 300 meters east words, he finds his shadow as 30 meters. His height is 6 meters. Then the height of the lamp post above the plane is in meters

 

 

Let OP be the lamp post and  , AB be the first position of the man with shadow AC=24m and LM be the second position of the man with shadow LN=30m
  
$OA=x,OL=\sqrt{x^2+{300}^2}\text{Now }△POC\text{ and }△ABC\text{ are similar }$ 
 ……..(1)
Similarly   are similar    
$$\begin{gathered} 5h=\sqrt{x^2+{300}^2}+30 \\ \Rightarrow {(5h-30)}^2=x^2+{300}^2 \end{gathered}$$ 
$$\begin{gathered} \Rightarrow {(5h-30)}^2={(4h+24)}^2+{300}^2 \\ \Rightarrow h^2-12h-9964=0 \\ \Rightarrow h=6\pm 100\Rightarrow h=106\text{ or }h=-94 \end{gathered}$$