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  1. GATE2019-2-GA-35
  2. GATE2019-2-GA-35
  3. GATE2019-2-GA-35
  4. GATE2019-2-GA-35

Two pipes P and Q can fill a tank in $6$ hours and $9$ hours respectively, while a third pipe R can empty the tank in $12$ hours.  Initially, P and R are open for $4$ hours, Then P is closed and Q is opened. After $6$ more hours R is closed. The total time taken to fill the tank (in hours) is  ____

  1. $13.50$
  2. $14.50$
  3. $15.50$
  4. $16.50$
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