A women with dollar bills go to the shopping he spent half of the money she had for shopping as she was so kind she gave one dollar to the beggar.she went to the hotel and spent half of the remaining and she gave 2 dollars to the waiter,the she buy some goods with half of the remaining and she gave 3 dollars to the receptionist. how much money she had in the beginning?Correct answer is '42'. Can you explain this answer?

Question

Answer

First she had 'x' dollars
spends half money on shopping ,so balance =x/2
1dollar for the beggar=x/2-1=x-2/2
remaining=x-2/2
spends 1/2in hotel x-2/2×1/2= x-2/4
2dollars for waiter ,x-2/4-2=x-10/4
1/2 dollar for shopping ,x-10/4-3= x-32/8
So total money ,x=
x-32/8=0
x-32=8
x=32+8
=42//

Hope this will help you

Answer

Given information:
- A woman goes shopping with a certain amount of money.
- She spends half of the money on shopping.
- She gives $1 to a beggar.
- She goes to a hotel and spends half of the remaining money.
- She gives $2 to a waiter.
- She buys some goods with half of the remaining money.
- She gives $3 to a receptionist.
- We need to find out how much money she had in the beginning.

Step-by-step solution:

Let's assume the amount of money the woman had in the beginning is 'x' dollars.

1. Spending on shopping:
- She spends half of the money, which is x/2 dollars.
- The remaining amount is x/2 dollars.

2. Giving money to a beggar:
- She gives $1 to the beggar.
- The remaining amount is (x/2) - 1 dollars.

3. Spending at the hotel:
- She spends half of the remaining amount, which is [(x/2) - 1]/2 dollars.
- The remaining amount is [(x/2) - 1]/2 dollars.

4. Giving money to a waiter:
- She gives $2 to the waiter.
- The remaining amount is [(x/2) - 1]/2 - 2 dollars.

5. Buying goods:
- She buys goods with half of the remaining amount, which is {[(x/2) - 1]/2 - 2}/2 dollars.
- The remaining amount is {[(x/2) - 1]/2 - 2}/2 dollars.

6. Giving money to a receptionist:
- She gives $3 to the receptionist.
- The remaining amount is {[(x/2) - 1]/2 - 2}/2 - 3 dollars.

According to the given information, the remaining amount of money at this stage is zero. So we can set up the equation:

{[(x/2) - 1]/2 - 2}/2 - 3 = 0

Simplifying the equation:

[(x/2) - 1]/2 - 2 = 6

[(x/2) - 1]/2 = 6 + 2

(x/2) - 1 = 8 * 2

(x/2) - 1 = 16

x/2 = 16 + 1

x/2 = 17

x = 17 * 2

x = 34

Therefore, the woman had 34 dollars in the beginning.

Similar Quant Doubts

A gave 25% of an amount to B. From the money B got, he spent 30% on a dinner. Out of the remaining amount, the respective ratio between the amount B kept as savings and the amount he spent on buying a book is 5 : 2. If B bought the book for Rs 460, how much money did A have in the beginning?

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