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If a 7-storey building has a 28 m long shadow, the number of storeys of the building whose shadow is 48 m long is:
Question

If a 7-storey building has a 28 m long shadow, the number of storeys of the building whose shadow is 48 m long is:

A.

14

B.

24

C.

16

D.

12

Correct option is D

Given:
​Height of the 7-storey building = unknown,
Shadow length of 7-storey building = 28 m
Shadow length of the unknown building = 48 m
Concept Used:
The shadow length is proportional to the height of the building.
Formula Used:
Height of Building 1Height of Building 2=Shadow Length of Building 1Shadow Length of Building 2\frac{\text{Height of Building 1}}{\text{Height of Building 2}} = \frac{\text{Shadow Length of Building 1}}{\text{Shadow Length of Building 2}}
Solution:
Let the number of storeys of the building with a 48 m shadow be "x". Since the shadow is proportional to the building height.
7x=28487×48=x×28x=33628=12\begin{aligned}&\frac{7}{x} = \frac{28}{48}\\ ​&7 \times 48 = x \times 28\\&x = \frac{336}{28} = 12\end{aligned}​​
Hence, the building with a 48 m shadow has 12 storeys.
Alternate Method:
By ratio method :
Number of storeysShadow length\text{Number of storeys} \propto \text{Shadow length}​​
7x=2848\frac{7}{x} = \frac{28}{48} ​​​
This directly gives x = 12.
Alternate Method 2: 
unitary method:

28m → 7 storey
48m → 7/28×48 = 12 storey

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