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  • Category: Quiz & Puzzles

    Can you solve this question?

    A person has three sisters. They are married and staying in the same village but in different areas. They are all wealthy. The person is poor.

    One day he went to his first sister's house. His sister counted the money he had in his pocket and added an equal amount in his pocket. While leaving her house, he offered the sister's daughter one rupee. From there he went to 2nd sister's house. There also his sister did the same thing. She counted the money in his pocket and added an equal amount of money to his pocket. While leaving her house he offered his sister's son one rupee. From there he went to his third sister's house. The same thing happened there also.

    He started back from his third sister's house and on the way, he counted the money in his pocket and found that it was only one rupee.

    Now the question was how much money he had in his pocket when he reached his first sister's house.
  • #777608
    Re. 1 is the answer.
    (a) Those who have forgotten Noakhali, how can they protest Sandeshkhali?
    (b) Have no fear of perfection - you'll never reach it. ---------- Salvador Dali

  • #777610
    Let us solve it using algebra.
    Let us assume that he had x money with him.
    After leaving the house of 1st sister he should have x + x -1 = 2x - 1 with him.
    After leaving 2nd sister he should have (2x -1) + (2x - 1) - 1 = 4x - 3 with him.
    After leaving 3rd sister he should have (4x - 3) + (4x - 3) - 1 = 8x -7 with him.
    But it is given that this last amount is equal to Rs 1.
    So 8x - 7 = 1
    Solving we get x = 1
    That is the answer.

    Thoughts exchanged is knowledge gained.

  • #777612
    There is yet another method to solve it which is by going in the reverse of the sequence that is starting from 'leaving the house of third sister' to 'entering the house of first sister'.
    After visiting the third sister he had Rs 1 which means he had Rs 2 before giving Rs 1 to the daughter of third sister. As the third sister added equal amount to what he had that means that he had only Rs 1 when he entered the house of third sister.
    With same reasoning and logic, we can go back further and find out that he had only Rs 1 when he entered the house of the first sister.

    Knowledge is power.

  • #777613
    Let's analyze the situation step by step.

    When he reached his first sister's house, let's say he had x rupees in his pocket.

    His sister added an equal amount, so now he has 2x rupees.
    He gave one rupee to his niece, so he has 2x - 1 rupees left.
    When he reached his second sister's house, he now has 2x - 1 rupees.

    His sister added an equal amount, so now he has 4x - 2 rupees.
    He gave one rupee to his nephew, so he has 4x - 3 rupees left.
    When he reached his third sister's house, he now has 4x - 3 rupees.

    His sister added an equal amount, so now he has 8x - 6 rupees.
    He didn't give any money to his niece or nephew this time.
    After visiting all three sisters, he starts back with 8x - 6 rupees. But on the way, he finds he only has 1 rupee left.

    So, 8x - 6 = 1
    => 8x = 7
    => x = 7/8

    Therefore, when he reached his first sister's house, he had (7/8) rupees in his pocket.

    Thanks & Regards
    Ekta Raikwar

    Make each day your masterpiece.

  • #777615
    # 77613,
    There is a misunderstanding.
    I mentioned in my post that in the third sister's house " The same thing happened there also."
    That means he gave one rupee there also. So 8X -7 =1 that means 8X = 8 so X = 1.
    The correct answer is One rupee.

    drrao
    always confident

  • #777616
    Respected Ekta Madam (#777613): you started well, but made a mistake at the third stage.
    (a) Those who have forgotten Noakhali, how can they protest Sandeshkhali?
    (b) Have no fear of perfection - you'll never reach it. ---------- Salvador Dali

  • #777619
    Let's break down the scenario:

    The person starts with a certain amount of money in his pocket (let's call this amount X).
    At each sister's house, the sister adds an equal amount of money to his pocket and he gives one rupee to each sister's child.
    Let's say the amount each sister adds to his pocket is Y rupees.

    So, after visiting the first sister, he has X + Y rupees in his pocket, and he gives 1 rupee to his niece, leaving him with (X + Y - 1) rupees.

    After visiting the second sister, he again receives Y rupees, and he gives 1 rupee to his nephew, leaving him with (X + Y - 1) + Y - 1 = X + 2Y - 2 rupees.

    Finally, after visiting the third sister, he receives Y rupees again, and he gives 1 rupee to his niece, leaving him with (X + 2Y - 2) + Y - 1 = X + 3Y - 3 rupees.

    However, he ultimately ends up with only 1 rupee in his pocket.

    So, we have the equation:

    X + 3Y - 3 = 1

    Solving for X:

    X = 4 - 3Y

    Since we know that the person ends up with only 1 rupee in his pocket after visiting the third sister, we can substitute Y = 1 into the equation:

    X = 4 - 3(1) = 4 - 3 = 1

    Therefore, when the person reached his first sister's house, he had 1 rupee in his pocket.

    Phagu Mahato
    Success occurs when opportunity and preparation meet.

  • #777622
    Yes, I understood my mistake. I am giving my other response.

    At the first sister's house: Let's say he had x rupees initially. His sister added an equal amount, making it 2x rupees. He then gave 1 rupee to his sister's daughter, so he was left with (2x - 1) rupees.

    At the second sister's house: He had (2x - 1) rupees from the previous house. His second sister added an equal amount, making it 2(2x - 1) rupees. He then gave 1 rupee to his sister's son, so he was left with (4x - 3) rupees.

    At the third sister's house: He had (4x - 3) rupees from the previous house. His third sister added an equal amount, making it 2(4x - 3) rupees. He then gave 1 rupee to his third sister's child, so he was left with (8x - 7) rupees.

    On his way back home, he counted his money and found only 1 rupee. Therefore, we can set up the equation:

    (8x - 7) = 1

    Solving for x:

    8x = 1 + 7
    8x = 8
    x = 1

    So, he initially had 1 rupee when he reached his first sister's house.

    Thanks & Regards
    Ekta Raikwar

    Make each day your masterpiece.

  • #777632
    I am happy that many members came out with correct answers but the approach is different. Paths are different and destination is the same. I congratulate all of them and thank them for their participation.
    drrao
    always confident


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