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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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