A TV tower 36 metres high casts a shadow of 24 metres at a particular time of a day. What is the height of a minar with a three metre high flagstaff atop it, if both of these together cast a shadow of 50 metres at the same time of the day?

### Concept & Direct Proportion The ratio of the height of an object to its shadow length is constant at a specific time of day. Find this constant ratio to determine unknown heights. $$ \text{Ratio} = \frac{\text{Height}}{\text{Shadow Length}} $$ ### Step-by-Step Solution * Calculate the constant height-to-shadow ratio from the TV tower: $\frac{36}{24} = 1.5$. * Let the height of the minar be $h$ metres. The total height of the minar and the flagstaff together is $(h + 3)$ metres. * Using the constant ratio for the minar and flagstaff combination: $\frac{h + 3}{50} = 1.5$. * Multiply to solve for the total height: $h + 3 = 1.5 \times 50 = 75$ metres. * Subtract the height of the flagstaff to find the minar's height: $h = 75 - 3 = 72$ metres. ### Exam Strategy & Shortcut Work purely in multiples. The height is $1.5 \times$ the shadow. So, total height for a $50$ m shadow is $50 \times 1.5 = 75$ m. Since the flagstaff is $3$ m, the minar is $75 - 3 = 72$ m. ### Common Pitfall Forgetting to subtract the 3-metre flagstaff from the total calculated height of 75 metres, which leads directly to the distractor option (c). ### Final Answer Therefore, the correct answer is **72 m**.