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GATE 2019 ME (ME2) – Question 7

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

P and Q fill a tank in 6 and 9 hours respectively; R empties it 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. Find the total filling time (hours).

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

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Correct answer: (B) 14.50

Explanation

First-stage net fill is $4(1/6-1/12)=1/3$. Second stage adds $6(1/9-1/12)=1/6$. Half remains, requiring $(1/2)/(1/9)=4.5$ hours. Total time is $4+6+4.5=14.50$ hours. **B**.