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A cistern can be filled by one of two pipes in 30 minutes and by the other in 36 minutes. Both pipes are opened together for a certain time but being particularly clogged only 5 / 6 of the full quantity of water flows through the former and only 9 / 10 through the later. The obstructions, however, being suddenly removed the cistern is filled in 15 1/ 2 minutes from that moment. How long was it before the full flow of water began?

Correct Answer: 1 minutes

Explanation:

Net filling in last 151/2 minutes
= 31/2 (1/30 + 1/36) = 341/360
Now, suppose they remained clogged for x minutes.
Net filling in these x minutes
= (x/30 x 5/6 + x/36 x 9/10) = 19 x/360
Remaining part = (1 - 19x/360) = (360 - 19x/360)
360 - 19x/360 = 341/360 or x = 1.
Hence, the pipes remained clogged for 1 minutes.


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