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 itp. 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

Let the amount available with lady is Rs x

Amount spend for hankies and given to bagger = \(\frac{x}2\)+1

Remaining amount = x - \((\frac{x}2+1)=\frac x2-1=\frac{x-2}2\)

Expences for lunch \((\frac{x-2}2)\times \frac 12\) = \(\frac{x-2}4\)

Amount of tip = Rs 2

Amount remained after lunch = \((\frac{x-2}2)-\frac{x-2}4-2\)

 = \(\frac{2x-4-x+2-8}4\) = \(\frac{x-10}4\)

Amounts spend for books = \(\frac 12\times\frac{x-10}4=\frac{x-10}8\)

Bus fare = Rs 3

Amount left = \(\frac{x-10}4-\frac{x-10}8-3\)

= \(\frac{2x-20-x+10-24}8=\frac{x-34}8\)

According to the question amount left = Re 1

\(\frac{x-34}8=1\)

On cross multiplication, we get

x - 34 = 8

x = 42

Therefore original amount with lady was Rs. 42