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 rupees tip. She spent half of the remaining amount on books 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

Step-by-step explanation:

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$\sf \green{Let : - }$

• Lady started with Rs. x

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

So, lady started with Rs. 42

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