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 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?

• A. 56
• B. 48
• C. 42
• D. 38

Answer 1

The correct option is C 42

Let the amount, a lady has in the begining

= ₹ $x$

In first case, amount spent $=\frac{x}{2}$

Given to begger = ₹1

$\therefore$ Balance = $x-(\frac{x}{2}+1)=x-\left(\frac{x+2}{2}\right)=\frac{2x-x-2}{2}$ = $\frac{x-2}{2}$

Amount spent on lunch $=\frac{x-2}{2}$ $\times$ $\frac{1}{2}$ = $\frac{x-2}{4}$

Given to tip = ₹2

$\therefore$ Balance $=\frac{x-2}{2}-(\frac{x-2}{4}+2)$

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

$=\frac{2(x-2)-(x-2)-2\times 4}{4}$

$=\frac{2x-4-x+2-8}{4}$

$=\frac{x-2-8}{4}=\frac{x-10}{4}$

Amount spent on purchase of a book

$=\frac{x-10}{4\times 2}=\frac{x-10}{8}$

Given as bus fare = ₹3

$\therefore$ Balance $=\frac{x-10}{4}-(\frac{x-10}{8}+3)$

$=\frac{x-10}{4}-\frac{x+10}{8}-3=\frac{x-10}{8}-3$

According to the condition :

$\frac{x-10}{8}-3=1$
$\Rightarrow \frac{x-10}{8}=1+3$

$\Rightarrow \frac{x-10}{8}=4$
$\Rightarrow x-10=32$
$\Rightarrow x=32+10=42$

The lady has ₹42 in the beginning.