Pipe A is capable of filling a tank in 16 minutes while Pipe B can fill the same tank in 24 minutes.
Pipe A is capable of filling a tank in 16 minutes while Pipe B can fill the same tank in 24 minutes. Both pipes are opened together, but after 4 minutes, the rate of Pipe A doubles and the rate of pipe B becomes half of its original. How many more minutes will it take to fill the completely?
पाइप A एक टैंक को 16 मिनट में भर सकता है जबकि पाइप B उसी टैंक को 24 मिनट में भर सकता हैं। दोनों पाइप एक साथ खोले जाते हैं, लेकिन 4 मिनट के बाद, पाइप A की दर दोगुनी हो जाती है और पाइप B की दर अपनी मूल दर से आधी हो जाती है टैंक को पूरी तरह से भरने में कितने मिनट और लगेंगे?
Detailed Solution & Logic
4min/ 4 मिनट
Solution
Initial filling rates:
Pipe A $=\dfrac{1}{16}$ tank/min
Pipe B $=\dfrac{1}{24}$ tank/min
Together,
$\dfrac{1}{16}+\dfrac{1}{24}=\dfrac{5}{48}$ tank/min
In the first $4$ minutes, they fill
$4\times\dfrac{5}{48}=\dfrac{5}{12}$
Remaining tank
$1-\dfrac{5}{12}=\dfrac{7}{12}$
After $4$ minutes:
- Pipe A's rate doubles $=\dfrac{2}{16}=\dfrac{1}{8}$
- Pipe B's rate becomes half $=\dfrac{1}{48}$
New combined rate
$\dfrac{1}{8}+\dfrac{1}{48}=\dfrac{7}{48}$ tank/min
Time to fill the remaining tank
$=\dfrac{\frac{7}{12}}{\frac{7}{48}}$
$=\dfrac{48}{12}$
=4 minutes
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