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Question

If a 1mm thick paper is folded so that the area is halved at every fold, then what would be the thickness of the pile after 50 folds?

A
100km
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B
1000km
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C
1millionkm
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D
1billionkm
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Solution

The correct option is C 1billionkm
Since the area is halved on folding, so each time the paper is folded in the centre i.e. its thickness becomes two-fold each time. So, we have :
Thickness after 1 fold =2mm;
Thickness after 2 folds =(2×2)mm=22mm;
Thickness after 3 folds =(22×2)mm=23mm; and so on.
Thickness after 50 folds =250mm=(2501000×1000)km.
Let x=250(1000)2. Then,
logx=50log22log1000=50×0.30102×3=9.0509.
So, x=antilog9=1000000000.
Hence, thickness after 50 folds =xkm=1billionkm.

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