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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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