Question

Hey friends please answer ⤵⤵
A lady went shopping and spent half of what she had on buying hankies and give 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 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

Final Answer :Rs. 42

Steps:
1) This type of Problem can be best worked out by making Tree Diagram.
(As shown in figure) .

2) Let us start with Rupees " P" with the lady.
Then, she frequently use it in the way related to money she used before.

After making tree diagram, we got at last the lady was remaining with [ (p-10)/8 -3] which is equal to 1 rupee as given in question.

$\frac{p - 10}{8} - 3 = 1 \\ = > \frac{p - 10}{8} = 4 \\ = > p - 10 = 32 \\ = > p = 42 \:$
Hence, Lady initially started with Rs. 42 .

Answer 2

Let x be the initial amount,
She spent half on buying hankies and gave one rupee to beggar

Amount left with her
=x/2  -1

Then she spent half on lunch and gave a 2 rupee tip

Amount left with her
x/4 - 1/2 -2
x/4 -  5/2

Then she spent half of remaining amount on book and 3 rupees on bus fair
So,
Amount left with her
=x/8 - 5/4 -3
=x/8 - 17/4
At the end she was left with 1 rupee so,
x/8 - 17/4 = 1
x/8 = 1 +17/4
x/8  = 21/4
x= 21 * 2
x= 42
So,
She had 42 rupees initially