question_answer

A vertical stick 15m long casts a shadow 12 m long on the ground. At the same time, a tower casts a shadow 50 m long on the ground. The height of the tower is

A) 60 m

B)  62 m    

C)  62.5 m

D)  63 m

Correct Answer: C

Solution :

Let AB be a vertical stick and AC be its shadow. Also, let PQ be a tower having shadow PR. As,        \[\Delta ABC\sim \Delta PQR\] \[\therefore \]                  \[\frac{AB}{PQ}=\frac{AC}{PR}\] \[\Rightarrow \]   \[\frac{15}{x}=\frac{12}{50}\]\[\Rightarrow \]\[x=\frac{15\times 50}{12}=62.5\,\,\text{m}\] Hence, height of the tower is 62.5 m.