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in Commercial Mathematics by (49.2k points)
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A pipe A can fill a tank in 27 min. Due to development of a hole in the bottom of the tank \(\frac{1}{10}\) of the water filled by pipe A leaks out. Find the time when the tank will be full. 

(a) 32 min 

(b) 34 min 

(c) 36 min 

(d) 30 min

1 Answer

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Best answer

(d) 30 min

In one minute \(\frac{1}{27}\) part of the tank is filled. Due to leak every minute, \(\frac{1}{10}\times\frac{1}{27}\) = \(\frac{1}{270}\) part of the tank leaks out. Hence the whole tank will be emptied in 270 min by the leak.

So, resultant work by pipe and leak in one min. 

\(\frac{1}{27}\) - \(\frac{1}{270}\)\(\frac{9}{270}\) = \(\frac{1}{30}\)

\(\therefore\) The tank will be filled in 30 min

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