Question

A lady went shopping and spent half of what she had on buying hankies and gave a rupee to a begger waiting outside the shop. She spent half of what was left on a lunch and followed that up with a two rupee tip. She spent half of the remaining amount on book and three rupees on bus fare. When she reached home, she found that she had exactly one rupee left. How much money did she start with?

Answer 1

Let x be the money she stared with

$\Rightarrow \frac{x}{2}$ spent on hankier & Rs.1 to beggar money remaining = $x[\frac{x}{2}+1]=\frac{x}{2}-1$

$\Rightarrow \frac{1}{2}(\frac{x}{2}-1)$ spent on lunch & Rs. 2 tip

$=\frac{x}{2}-1-[\frac{1}{2}(\frac{x}{2}-1)+2]$

$=\frac{x}{4}-\frac{5}{2}$

$\Rightarrow \frac{1}{2}(\frac{x}{4}-\frac{5}{2})$ on book and Rs.3 on fare.

$\frac{x}{4}-\frac{5}{2}-[\frac{1}{2}(\frac{x}{4}-\frac{5}{2})+3]$

$=\frac{x}{8}-\frac{7}{4}=1$

$\frac{x}{8}=1+\frac{14}{8}$

$\frac{x}{8}=\frac{22}{8}$

$x=Rs.22$