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lovesuit
Three pumps X, Y, and Z drain the water tank for 2,3, and 6 hours respectively. if the size of the water tank is doubled and all pumps work together to drain the water tank takes 2 hours. 2 pumps A and B pump water into the tank. All 5 pumps working together drain the water tank in 3 hours. How much time will pump A and B will take to fill the water tank if the water tank is empty and X, Y, and Z are not working?(doubled size tank)

A. 4 hours
B, 6 hours
C. 8 hours
D. 10 hours
E. 12 hours

PS: I am uploading for the first time so feel free to tell me, if I have made a mistake or mistakes.


If all 3 pumps drain the water tank, it will take 1 hour to drain the tank (1/2 + 1/3 + 1/6)

If the size of the tank is doubled, the time taken to drain will also be doubled if only these 3 pipes are operational = 2 hours ( also mentioned in the question)

If A and B fill the this doubled size tank, and suppose they take A and B hours respectively, then -

1/2 - (1/A + 1/B) = 1/3 ( 2 hours drain time increases to 3 hours due to pipes A and B)

Hence, 1/A + 1/B = 1/6


Answer = 6 hours
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x + y + z = 1/2 + 1/3 + 1/6 = 1
Work rate of the outlet pipes

Now, Drainage = Outlet - Inlet
So, x + y + z - (a+b) = Twice the capacity/ Total Time
1 - (a+b) = 2/3
Therefore, (a+b) = 1/3 = Work done / Total Time
1/3 = 2/ Total Time
Hence, Time combined while only a and b are working = 6 hours.
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Just a poorly written question. Could someone please direct me to a similar-sounding, but accurately worded question?
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rajatyadav1994
Just a poorly written question. Could someone please direct me to a similar-sounding, but accurately worded question?
Here's a link to all the Work/Rate problems where you may encounter similar question: https://gmatclub.com/forum/search.php?s ... &tag_id=66
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