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 of 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

Answer:

she start with 42 rs

Step-by-step explanation:

let she had X rs at starting

Now she spent half on shopping that is X/2 and gave 1 rs to begger

Now she have( X/2 - 1 )rs now she spent half on launch then she have [X-2]/4 also she gave 2 rs tip now she have [X-2-8]/4

naw she spen half on buying books

then she have left with [X-10]/8 now she gave 3rs buss fair tge she left with rs [X-10-24]/8 rs

but when she reach home she had only 1 rs

hence,

[X-34]/8 =1

[X-34] = 8

X = 8+34

X = 42 .

Answer 2

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$\sf \green{Let : - }$

Lady started with Rs. x

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$\begin{gathered} \rm \: Money \: spent \: on \: hankies \\ \twoheadrightarrow \bf \: \frac{x}{2} \\ \\ \rm Remainder = x - \frac{x}{2} \\ \twoheadrightarrow \bf \frac{2x - x}{2} \\ \twoheadrightarrow \bf \frac{x}{2} \\ \\ \rm \: Money \: spent \: to \: beggar \\ \twoheadrightarrow \bf \: rs. \: 1 \\ \\ \rm \: Remainder = \frac{x}{2} - 1 \\ \twoheadrightarrow \bf \frac{x - 2}{2} \\ \\ \rm \: Money \: spent \: on \: lunch \\ \twoheadrightarrow \bf \frac{x - 2}{4} \\ \\ \rm \:Remainder = \frac{x - 2}{2} - \frac{x - 2}{4} \\ \twoheadrightarrow \bf \: \frac{x - 2}{4} \\ \\ \rm \: Money \: spent \: on \: tip = rs.2 \\ \\ \rm \: Remainder = \frac{x - 2}{4} - 2\\ \twoheadrightarrow \bf \: \frac{x - 2 - 8}{4} \\ \twoheadrightarrow \bf \frac{ x - 10}{4} \\ \\ \rm \: Money \: spen t \: on \: books \\ \twoheadrightarrow \bf \frac{x - 10}{8} \\ \\ \rm \: Remainder = \frac{x - 10}{4} - \frac{x - 10}{8} \\ \twoheadrightarrow \bf \frac{x - 10}{8} \\ \\ \rm \: Money \: spent \: on \: bus \: fare \\ \twoheadrightarrow \bf rs. \: 3 \\ \\ \rm \: Remainder = \frac{x - 10}{8} - 3 \\ \twoheadrightarrow \bf \frac{x - 10 - 24}{8} \\ \twoheadrightarrow \bf \frac{x - 34}{8} \\ \\ \bold{ \bigstar \: ACQ} \\ \therefore \: \tt \frac{x - 34}{8} = 1 \\ \tt \dashrightarrow \: x - 34 = 8 \\ \dashrightarrow \tt \boxed{ \tt \: x = 42}\end{gathered}$

So, lady started with Rs. 42

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