Question

A 50 metres high tower casts a shadow 30 metres long on the ground at a certain time and at the same time, if a light house casts a shadow 60 metres long, then the height of light house is

• A. 50m
• B. 100 m
• C. 75 m
• D. 150 m

Answer 1

The correct option is B 100 m

Let the height of the light house be h.



$\angle BCA=\angle EFD$ (As both the shadows are cast at the same time)
$\angle B=\angle E$ ( Each ${90}^0$)
$\Delta ABC\sim \Delta DEF$ (AA similarity criterion)
$\Rightarrow \frac{AB}{BC}=\frac{DE}{EF}$
$\Rightarrow \frac{50}{30}=\frac{h}{60}$
$\Rightarrow h=100m$
Hence, the correct answer is option (2)