A pipe can fill a tank in 2\frac{2}{3} hours, and another pipe empties it in 4 hours. If both are opened together, how long will it take to fill the tank?
A pipe can fill a tank in $2\frac{2}{3}$ hours, and another pipe empties it in 4 hours. If both are opened together, how long will it take to fill the tank?
एक पाइप टंकी को $2\frac{2}{3}$घंटे में भर सकता है, और दूसरा पाइप उसे 4 घंटे में खाली कर सकता है। यदि दोनों पाइप एक साथ खोल दिए जाएँ, तो टंकी को भरने में कितना समय लगेगा?
Detailed Solution & Logic
Correct Answer:
8h/ घंटे
Time taken by filling pipe = $2\frac{2}{3}$ hours
$2\frac{2}{3} = \frac{8}{3}$ hours
Filling rate of pipe A:
$= \frac{1}{8/3} = \frac{3}{8}$ tank per hour
Emptying rate of pipe B:
$= \frac{1}{4}$ tank per hour
Net filling rate when both are opened:
$= \frac{3}{8} - \frac{1}{4}$
$= \frac{3}{8} - \frac{2}{8}$
$= \frac{1}{8}$ tank per hour
Time to fill the tank:
$= \frac{1}{1/8} = 8$ hours
Answer: 8 hours
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