Question

The Qutub Minar casts a shadow $150\text{m}$ long, at the same time the Vikas Minar casts a shadow $120\text{m}$ long on the ground. If the height of the Vikas Minar is $80\text{m}$, find the height of the Qutub Minar.

• A. $180\text{m}$
• B. $100\text{m}$
• C. $150\text{m}$
• D. $120\text{m}$

Answer 1

The correct option is B $100\text{m}$

$\text{Since both the Qutub Minar and the Vikas Minar cast the shadow at the same time,the elevation}\alpha \text{is same for both so}\text{far as the shadow cast by the sun is concerned}.\text{Given V=80 m, height of Vikas Minar}\text{R=120 m, shadow of Vikas Minar}\text{S=150 m, shadow of Qutub Minar}\text{Q=?, height of Qutub Minar}\text{now},\frac{\text{V}}{\text{R}}=\tan \alpha \therefore \tan \alpha =\frac{80}{120}=\frac{2}{3}\left(\text{for Vikas Minar}\right)\therefore \text{for Qutab Minar},\frac{\text{Q}}{\text{S}}=\tan \alpha =\frac{2}{3}⟹\text{Q}=\frac{2}{3}\times \text{S}⟹\text{Q}=\frac{2}{3}\times 150=100\text{m}$