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      Question

      Rs. 5625 is divided among A, B and C so that A receives

      one half as much as B and C together receive and B receives one-fourth of what A and C together receive. The share of A is more than that of B by:
      A Rs. 750 Correct Answer Incorrect Answer
      B Rs. 775 Correct Answer Incorrect Answer
      C Rs. 1500 Correct Answer Incorrect Answer
      D Rs. 160 Correct Answer Incorrect Answer

      Solution

      Total = Rs. 5625

      A = (1/2}) x (B + C)

      B = (1/4}) x (A + C)

      Let B = x

      A + C = 4 x ⇒C = 4x – A …(1)


      A = 1/2 (B + C) = 1/2 (x + C) ⇒ 2A = x + C ….(2)

      Substitute C from (1) into (2):

      2A = x + (4x − A) ⇒ 2A = 5x – A


      ⇒ 3A = 5x ⇒A = 5x/3

      Now, C = 4x – A = 4x − 5x/3 = (12x − 5x)/3 = 7x/3

      A + B + C = (5x/3) + x + (7x/3) = 15x/3 =5x


      5x = 5625 ⇒x = 1125


      A = 5x/3 = (5 × 1125)/3 =1875


      A – B = 1875 – 1125 = 750

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