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    Question

    Soham says, "I have as many sisters as brothers." Pooja

    says, "Each of us sisters has only half as many sisters as brothers." Assuming that Soham and Pooja are brother and sister, how many brothers and sisters does the family have?
    A 4 brothers and 6 sisters Correct Answer Incorrect Answer
    B 6 brothers and 4 sisters Correct Answer Incorrect Answer
    C 3 brothers and 4 sisters Correct Answer Incorrect Answer
    D 4 brothers and 3 sisters Correct Answer Incorrect Answer

    Solution

    Let no. of brother be X and no. of sister be Y. As Sohan says "I have as many sister as brothers" ⇒ (X - 1) = Y -----(1) (He himself be not counted) as Pooja says "Each of us sister has only half as many sister as brothers". ⇒ Y - 1   = 0.5  × X ----- (2) (She herself be not counted) Solving both equation, Rearranging (1)  ⇒ X = Y + 1   --------- (3) Substituting (3) into (2)  ⇒ Y - 1 = 0.5  × (Y + 1) -------- (4) Solving (4) ⇒ 2Y - 2 = Y + 1 ⇒   Y = 3 Substituting Y = 3 into (3)  We get: X = 3 + 1 =  4 Therefore, answer is 3 Sister and 4 brother Hence, the correct answer is  "4 brothers and 3 sister".

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