Question

A lady went
for shopping and spent half of what she had on buying hankies and give a Rupee to a bigger waiting outside the shop she spend half of what was left on a lunch and followed that up with a tooltip she spent half of the remaining amount on a book and 3 rupees on bus fare when she reached home she found that she had exactly one left how much money did she start with?

Answer 1

Answer: 42 rupees

Step-by-step explanation:

Let m be amount she starts with

She spent m/2 for hankies and remaining is m/2

Gave a rupee for a beggar, so remains m/2 - 1

she spent (m/2 - 1)/2 for lunch so remains (m/2 - 1)/2

gave 2 rupees as tip, so remains (m/2 - 1)/2 -2

spent half of the remaining for book. so she spent [(m/2 - 1)/2 -2]/2 for book

The remaining amount in her hand = [(m/2 - 1)/2 -2]/2

Spent 3 for bus fare, so remains  [(m/2 - 1)/2 -2]/2 -3

But she is left with 1 rupee

So [(m/2 - 1)/2 -2]/2 -3= 1

[(m/2 - 1)/2 -2]/2=4

(m/2 - 1)/2 -2=8

(m/2 - 1)/2=10

m/2 - 1=20

m/2=21

m=42

So she started with 42 Rs

----------------------------------------------------

Another method

She is left with 1 rupee after spending the bus fare. So before that she had 4 rupees with her. This is the remaining after spending half of what she has before buying book. So before buying book she had 8 rupees with her. likewise before giving the tip of 2 rupees she had 10 rupees with her.

Before lunch ----20

before giving to beggar -----21

before buying hankies -----42