Question

If we fold a piece of paper 42 times, its thickness will actually be equal to the distance between the Earth and the Moon. How many more times do we have to fold a piece of paper so that its thickness is twice the distance between the Earth and the Moon?

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is B 1

Let the thickness of the paper be T
After folding for the first time, its thickness becomes $2$T.
Next, we fold for the second time, and the thickness becomes = $2\times 2$ T= $2^2$T
Similarly, after foldering it for three times, the thickness becomes = $2\times 2^2$ T = $2^3$T
.
.
.
.
(We can see a pattern here)

Hence, after folding 42 times,the folded paper's thickness is $2^{42}$T.
Now, folding it 43 times, thickness = $2^{43}$T = $2\times 2^{42}$T
We know that the distance between the Earth and the Moon is $2^{42}$T, and the thickness of the paper after folding 43 times is
$2^{43}$T
=$2\times 2^{42}$T
=$2\times$(Distance between the Earth and the Moon)

To get the twice of the distance between the Earth and the Moon, we need to fold the paper 43 times, i.e., $43-42=1$ extra fold, we need to make to double the distance.