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To construct a wall, sand and cement are mixed in the ratio of $3: 1$. The cost of sand and that of cement are in the ratio of $1:2.$

If the total cost of sand and cement to construct the wall is $1000$ rupees, then what is the cost (in rupees) of cement used?

  1. $400$
  2. $600$
  3. $800$
  4. $200$
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