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In a bag there are total of $150$ coins in three denominations $₹1,₹2$ and $₹5$ with at least one coin of each denomination being present in the bag. The total value of the Re.$1$ coins is at least $50\%$ of the total value of the coins in the bag. If there are $23\:₹5$ coins in the bag and the total value of the $₹2$ coins is at least $3\%$ of the total value of the coins in the bag, find the number of $₹2$ coins in the bag.

  1. $2$
  2. $3$
  3. $4$
  4. $1$
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