Pipe A can fill a tank in 18 hours, pipe B can fill the same tank in 21 hours and pipe C can fill the same tank in 16 hours. The time taken by them to fill the same tank if they operate together is::
Pipe A can fill a tank in 18 hours, pipe B can fill the same tank in 21 hours and pipe C can fill the same tank in 16 hours. The time taken by them to fill the same tank if they operate together is::
पाइप A किसी टंकी को 18 घंटे में भर सकता है, पाइप B उसी टंकी को 21 घंटे में भर सकता है और पाइप C उसी टंकी को 16 घंटे में भर सकता है। यदि वे सभी एक साथ चालू कर दिए जाएँ, तो उस टंकी को भरने में कितना समय लगेगा?
Detailed Solution & Logic
Correct Answer:
\(6\frac{6}{167}\) घंटे
Solution:
Rates:
Pipe A = $ \frac{1}{18} $, Pipe B = $ \frac{1}{21} $, Pipe C = $ \frac{1}{16} $
Combined rate:
LCM of 18, 21, 16 = 1008
$ \frac{1}{18} = \frac{56}{1008}, \quad \frac{1}{21} = \frac{48}{1008}, \quad \frac{1}{16} = \frac{63}{1008} $
So,
$ \frac{56 + 48 + 63}{1008} = \frac{167}{1008} $
Time taken:
$ \text{Time} = \frac{1008}{167} = 6\frac{6}{167} $
Final Answer: $6\frac{6}{167}$ घंटे
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