# A lady went shopping and spent half of what she had on buying hankies and gave a rupee to a beggar waiting outside the shop.

Question:

A lady went shopping and spent half of what she had on buying hankies and gave a rupee to a beggar 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 a 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?

Solution:

Suppose, the lady start ed with x rupee $s$.

Money spent on shopping $=\frac{x}{2}$ rupees

Remaining amount $=\mathrm{x}-\frac{\mathrm{x}}{2}=\frac{\mathrm{x}}{2}$ rupee $\mathrm{s}$

After giving a rupee she had $=\left(\frac{\mathrm{x}}{2}-1\right)$ rupees

Money spent on lunch $=\frac{1}{2}\left(\frac{\mathrm{x}}{2}-1\right)$ rupees

After giving $a$ two $-$ rup $e e$ tip she had $=\frac{1}{2}\left(\frac{\mathrm{x}}{2}-1\right)-2=\frac{\mathrm{x}-2-8}{4}=\frac{\mathrm{x}-10}{4}$ rupees

Money spent on a book $=\frac{1}{2}\left(\frac{\mathrm{x}-10}{4}\right)$ rupees

After spending three rupees on bus fare she had $=\frac{1}{2}\left(\frac{\mathrm{x}-10}{4}\right)-3=\frac{\mathrm{x}-10-24}{8}=\frac{\mathrm{x}-34}{8}$ rupees

Now,

$\frac{\mathrm{x}-34}{8}=1$

or $\mathrm{x}-34=8$

or $\mathrm{x}=42$

Therefore, she start ed with 42 rupees.