A shopkeeper bought $80$ kg of sugar at Rs. $13.50$ per kg and mixed it with $120$ kg of sugar at Rs. $16$ per kg. To gain $16\%$, at what price per kg should he sell the mixture?
Options:
- A: Rs. $18$
- B: Rs. $17.40$
- C: Rs. $16.50$
- D: Rs. $17.50$
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