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.
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?
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.