A lady went shopping and spent half of what she had on buying hankies and gave a rupee to a begger w...

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 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

Accepted Answer

Let the amount lady had be Rs x

Amount spent for hankies and given to begger is x/2 + 1

Remaining amount is x – (x/2 + 1) = x/2 – 1 = (x-2)/2

Amount spent for lunch (x-2)/2×1/2 = (x-2)/4

Amount given as tip is Rs 2

Remaining amount after lunch = (x-2)/2 – (x-2)/4 – 2 = (2x – 4 – x + 2 - 8)/4 = (x - 10)/4

Amounts spent for books =1/2 × (x-10)/4 = (x-10)/8

Bus fare is Rs 3

Amount left = (x-10)/4 – (x-10)/8 – 3 = (2x – 20 – x + 10 – 24)/8 = (x-34)/8

So from the question we know that the amount left = Rs 1

(x-34)/8 = 1

By cross-multiplying we get,

x – 34 = 8

x = 8 + 34

= 42

∴ the lady started with Rs. 42

RD Sharma Solutions Class 8 Mathematics Solutions for Linear Equation in One Variable Exercise 9.4 in Chapter 9 - Linear Equation in One Variable