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?

Answer 1

Suppose, the lady started with x rupees.
Money spent on shopping \[= \frac{x}{2}\text{ rupees }\]
Remaining amount\[ = x - \frac{x}{2} = \frac{x}{2} \text{ rupees }\]
After giving a rupee she had \[= (\frac{x}{2} - 1) \text{ rupees }\]
Money spent on lunch\[= \frac{1}{2}(\frac{x}{2} - 1) \text{ rupees }\]
After giving a two - rupee tip she had \[= \frac{1}{2}(\frac{x}{2} - 1) - 2 = \frac{x - 2 - 8}{4} = \frac{x - 10}{4} \text{ rupees }\]
Money spent on a book \[= \frac{1}{2}(\frac{x - 10}{4}) \text{ rupees }\]
After spending three rupees on bus fare she had \[= \frac{1}{2}(\frac{x - 10}{4}) - 3 = \frac{x - 10 - 24}{8} = \frac{x - 34}{8} \text{ rupees }\]
Now, 
\[\frac{x - 34}{8} = 1\]
or x - 34 = 8
or x = 42
Therefore, she started with 42 rupees .