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Three pipes A, B and C can till a cistern 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 cistern is :
A) 12
B) 14
C) 16
D) 18
Correct answer:
B) 14
Description for Correct answer:
Part of the tank filled by three pipes (A + B + C) in 1 hour = \( \Large \frac{1}{6} \)
\( \Large \therefore \) Part filled by in 2 hour = \( \Large \frac{2}{6} = \frac{1}{3} \)
\( \Large \therefore \) Remaining part = \( \Large 1 - \frac{1}{3} = \frac{2}{3} \)
Part filled by (A + B) in 7 hours = \( \Large \frac{2}{3} \)
\( \Large \therefore \) (A + B )'s 1 hour's work = \( \Large \frac{2}{21} \)
\( \Large \therefore \) Part filled by C in 1 hour
= Part filled by (A + B + C) in 1 hour - Part filled by (A + B) in 1 hour
= \( \Large \frac{1}{6} - \frac{2}{21} = \frac{14 - 8}{84} = \frac{6}{84} = \frac{1}{14} \)
\( \Large \therefore \) C alone can fill the tank in 14 hours
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