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    A large rectangular paper having sides in the ratio of 3:8 is cut in half across the longer side. The process is repeated several times. At which stag
    Question

    A large rectangular paper having sides in the ratio of 3:8 is cut in half across the longer side. The process is repeated several times. At which stages of the repeated cuttings will the ratio of the sides be 3:8?

    A.

    Never

    B.

    Every second cut

    C.

    Every third cut

    D.

    Every fifth cut

    Correct option is A

    Solution:

    Initially, the paper has sides in the ratio of 3:8. When it is cut in half across the longer side, the longer side becomes half its previous length while the shorter side remains the same.

    After the first cut:

    The new dimensions of the rectangle become 3:4 (as the long side has been halved).

    After the second cut:

    The dimensions become 3:2 (since the long side is halved again).

    After the third cut:

    The dimensions become 3:1 (again halved along the long side).

    The ratio 3:8 can never be restored in the following cuts, as the ratio keeps changing in each step by halving the longer side. Thus, after cutting, the ratio will never revert to 3:8 again.

    Therefore, the answer is Never.

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