# Question 11 & 12

**Question 11: 1 millimeter thick paper if folded 50 times then find the thickness of the fold.**

**FPSC AD IB 2018**

**Solution:**

We know

and

or

or

So, we can other way say that;

so, 1 millimeter is equal to 0.000001 kilometer

or we can say that single paper is 0.000001 km thick

If we fold this paper one time then there will be two layers of papers;

**One time folding**

times of 0.000001

**Second time folding,** (there will be four layers of papers)

**Third time folding **( there will be 8 layers of papers)

**Fourth time folding **(there will be 16 layers of paper)

,,,,,,,,,,,,,,,,,,,,,, so on ,,,,,,,,,,,,,,,,,,>,,,,,,,,,,,,,,,,,so on,,,,,,,,,,,,,,,,,,,>,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,>,,,,,,,,, so on ,,,,,,,,,,,,,,,,,,,,,,,,>,,,,,,,,,,,,,,,,,,,,,,,,,,,, till

**Fiftieth time folding**

Now let’s evaluate the term =

**So, if a paper of 1 mm thickness is folded 50 times then it’s thickness will be equal to 11258999906.842624 kilometers**

**Or 112 billion kms approximately**

**Question 12: Total age of 3 men if added is 80 years. What was the sum three years ago?**

**FPSC AD IB 2018**

**Solution: **

Let there be three persons A, B and C and their ages at present be x, y and z, Then according to the given condition;

Three years ago the ages of A, B and C was x-3, y-3 and z-3 respectively. Now the sum of ages three years ago will be;

Now let us simplify this term;

Sum of ages three years ago =

Putting value of x+y+z from eq (1)

**So sum of ages three years ago is 71**