Question

A lady starts from her house with some money to visit four Churches.

1. As soon as she enters Church1 her money gets doubled. She donates $100 and moves.
2. At Church2 again her money is doubled and she donates $100.
3. Her money is doubled again at Church3 and she donates $100.
4. At Church4 again her money gets doubled. She donates $100 again and returns home empty handed…

How much money she had when she started from her house???

Answer 1

93.75
Money after Church 1: 187.5-100 = $87.5
Money after church 2: 175-100 = $75
Money after church 3: 150-100 = $50
Money after church 4: 100-100 = 0

Answer 2

Suppose the lady has $X . Initially.
When she went to first church, her money gets doubled. So she has $2X ,of which she donated $100 .

So before going to 2nd church she has $(2x-100)
Similarlly, in 2nd church doubled money will be 2(2x-100), after donating $100, She left with $(4x-300)
In 3rd church doubled money will be 2(4x-300), after donating $100, remaining money is $(8x-700)
In 4th church again doubled money will be 2(8x-700),after donating $100, the money left is $(16x-1500)=0
hence, 16x=1500,so x=$93.75

So initially she has $93.75