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. $100km$
• B. $1000km$
• C. $1millionkm$
• D. $1billionkm$

Answer 1

Answer: (D)

$1billionkm$

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 $=(2\times 2)mm=2^{2}mm$;
Thickness after $3$ folds $=(2^2\times 2)mm=2^{3}mm$; and so on.
$\therefore$ Thickness after $50$ folds $=2^{50}mm=\left(\frac{2^{50}}{1000\times 1000}\right)km$.
Let $x=\frac{2^{50}}{{\left(1000\right)}^2}$. Then,
$\log x=50\log 2-2\log 1000=50\times 0.3010-2\times 3=9.050\sim 9$.
So, $x=anti\log 9=1000000000$.
Hence, thickness after $50$ folds $=xkm=1billionkm$.