two pipes P and Q can fill a tank independently in 12hours and 18hours respectively. if the tank is already 7/12th full and both the pipes are opened simultaneously, in how much time they can fill the remaining tank
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Volume filled by p in 1 hr = 1/12
Volume filled by Q in 1 hr = 1/18
Volume filled by both A and B in 1 hr = 1/12 + 1/18
⇒ Volume filled by both A + B in 1 hr = (3 + 2)/36
⇒ Volume filled by both (A + B) in 1 hr = 5/36
Total Time to fill the tank = (Total volume of the tank)/(Volume filled by both (A + B) in 1 hr)
⇒ Total Time to fill the tank = 1/(5/36)
⇒ Total Time to fill the tank = 36/5 hr
⇒ Total Time to fill the tank = 7 hours 12 minutes
∴ The total time to the filled the empty tank is 7 hours 12 minutes.
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