Question
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:
Answer: Option C
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Part filled in 2 hours = \(\frac{2}{6} =\frac{1}{3}\)
Remaining part = \(\left(1-\frac{1}{3}\right) =\frac{2}{3}\)
So, (A + B)'s 7 hour's work = \(\frac{2}{3}\)
(A + B)'s 1 hour's work = \(\frac{2}{21}\)
So, C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }
= \(\left(\frac{1}{6}-\frac{2}{21}\right)=\frac{1}{14}\)
So, C alone can fill the tank in 14 hours.
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