Earth Shaking Puzzle

Interesting question but the way it was phrased may lead to many misinterpretation.

let x amount he was having. so x he borrowed. after purchasing pen amount remain=2 x-100. this remaining amount again he has to borrow after purchasing vase amount remaining=(2 (2 x)-100) -100. this remaining amount again he has to borrow similarly after purchasing wallet amount remaining= (2 (2 (2 x)-100)-100)-100=0. solve for x=87.5.

Let x be his original amount. He borrowed x & buys a pen worth 100. So he is left with 2x - 100.

Assume it to be y. ie 2x = 100 + y

By the same process 2y = 100 + z

2z = 100 + 0

Hence z = 50

y = (100+z)/2 = (100+50)/2 = 75

x = (100 + y)/2 = (100 + 75)/2 = 87.5

Let his money = $x$ .

At the first situation, $x<100$ . So he borrowed x amount of money,

$2x>100$

The reminder of the money is $2x-100$ which is more than $0$ , so

$2x-100>0$

And then do the same process twice.

$2x-100<100$

$4x-200>100$

$4x-300>0$

But in this process...

$4x-300<100$

$8x-600=100$

It's equal to 100 because after this, he got no money left.

$8x-700=0$

Find the value of x: $x=\frac{700}{8}=87.5$

for last case- 50+50=100 so we know before buying last item he had only 50 left with him. 2nd case- 2x-100=50 hence x=75 so in 2nd case he started with 75 similarly in first case money that he had =2y-100=75 hence y=175/2=87.5

What do you think about this solution?

$\frac{100}{2} = 50$ ----> last money to buy the third item

$\frac{50+100}{2} = 75$ ----> before the second item was bought

$\frac{75+100}{2} = \boxed{85}$ ----> original money in hand