Question
Option 4 : $6$ hours
Detailed Solution
सही उत्तर $6$ hours है।
prepsnap.in • Part -AQuestion:
Pipe A can fill a tank in $12$ hours, pipe B in $18$ hours, and pipe C can empty the full tank in $24$ hours. All three are opened together; after some time pipe C is closed, and the tank is found to be exactly full after $9$ hours from the start. For how many hours was pipe C open? / पाइप A टंकी को $12$ घंटे में, B $18$ घंटे में भर सकता है, और C भरी टंकी को $24$ घंटे में खाली करता है। तीनों एक साथ खोले गए; कुछ समय बाद C बंद कर दिया गया और शुरू से $9$ घंटे में टंकी ठीक भर गई। C कितने घंटे खुला रहा?
Correct Answer: $6$ hours
With all three open the rate is $\frac{1}{12}+\frac{1}{18}-\frac{1}{24} = \frac{7}{72}$/h; with C closed it is $\frac{1}{12}+\frac{1}{18} = \frac{10}{72}$/h. If C was open for $t$ hours: $\frac{7t+10(9-t)}{72} = 1 \Rightarrow 90-3t = 72 \Rightarrow t = 6$. / समीकरण $7t+10(9-t)=72$ से $t=6$ घंटे। Option (c) is the trap for those who use only A and B for the whole $9$ hours and ignore C's negative contribution.