A sum of Rs. 6000 is distributed among A, B, and C. A gets 2/3 of what B and C…

Answer: Rs. 2100

Let A, B, C be the shares. Given A + B + C = 6000, A = (2/3)(B + C), and C = (1/3)(A + B).

• Use B + C = 6000 − A and substitute into A = (2/3)(B + C):

  A = (2/3)(6000 − A) ⇒ 3A = 2(6000 − A) ⇒ 3A = 12000 − 2A ⇒ 5A = 12000 ⇒ A = 2400

• Use A + B = 6000 − C and substitute into C = (1/3)(A + B):

  C = (1/3)(6000 − C) ⇒ 3C = 6000 − C ⇒ 4C = 6000 ⇒ C = 1500

• Now find B:

  B = 6000 − A − C = 6000 − 2400 − 1500 = 2100

Thus B's share is Rs. 2100.