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 lunch and followed that up with a two rupee tip. She spent half of the remaining amount on the 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

Assume that the lady started with $Rsx.$

Step 1: Find the amount left with her in terms of $x.$

At shopping, she spent half of what she had

Therefore, remaining amount $=x-\frac{x}{2}=\frac{x}{2}$

She gave $Rs.1$ to the beggar.

Now, the remaining amount$=\frac{x}{2}-1$

She spent half of the remaining at lunch followed by $Rs.2$ tips.

Hence, remaining $=\frac{\left({\displaystyle \frac{x}{2}}–1\right)}{2}–2=\frac{x-2}{2\times 2}-2=\frac{x-2}{4}-2=\frac{x-10}{4}$

Again, she spent half of the remaining on book and $Rs.3$ for bus fare.

Thus, remaining $=\frac{x-10}{4\times 2}-3=\frac{x-34}{8}$

Step 2 : Find the value of $x.$

Finally, she has $Rs.1$ left with her.

So, $\frac{x-34}{8}=1$

$$\begin{gathered} \Rightarrow x-34=8 \\ \Rightarrow x=42 \end{gathered}$$

Hence, the lady started with $Rs42$