GATE ME 2019 Set 2 — Question 7
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General Aptitude → Quantitative Aptitude → Time & Work
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Question
Two pipes and can fill a tank in 6 hours and 9 hours respectively, while a third pipe can empty the tank in 12 hours. Initially, and are open for 4 hours. Then is closed and is opened. After 6 more hours is closed. The total time taken to fill the tank (in hours) is ______.
Correct answer
(B) 14.50
Solution
Let the capacity of the tank be the LCM of 6, 9, and 12, which is 36 units.
Work done = units.Step 2: Next 6 hours ( closed, and open)
Work done = units.Step 3: Total work done after 10 hours
Total work = units.
Remaining work = units.Step 4: Final stage ( closed, only open)
Time taken by to fill the remaining 18 units = hours.Step 5: Total time
Total time = hours.
- Rate of pipe units/hr
- Rate of pipe units/hr
- Rate of pipe units/hr (negative because it empties)
Work done = units.Step 2: Next 6 hours ( closed, and open)
Work done = units.Step 3: Total work done after 10 hours
Total work = units.
Remaining work = units.Step 4: Final stage ( closed, only open)
Time taken by to fill the remaining 18 units = hours.Step 5: Total time
Total time = hours.
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