a tank can be filled by two taps A and B in 12 hours and 16 hours respectively the full tank can be emptied by a third Tapsee in 8 hours how long will it take to fill the tank if all the taps are open question mark
Answers
Answer:
Tap A can fill tank in 12 hrs
Tap A can fill tank in 1 hour = \frac{1}{12}
Tap B can fill tank in 16 hrs
Tap B can fill tank in 1 hour = \frac{1}{16}
Tap C can empty the tank in -8hrs
Tap C can empty tank in 1 hour = \frac{1}{8}
We are given that The ful tank can be emptied by a third tap
Tap (A+B+C)'s 1 hr work = \frac{1}{12}+\frac{1}{16}-\frac{1}{8}
=\frac{1}{48}
So, Total time taken by A and B and C = \frac{48}{1}
So, if all the taps are opened the tank will be filled in 48 hours
Step-by-step explanation:
Tap A can fill tank in 12 hrs
Tap B can fill tank in 16 hrs
Tap C can empty the tank in -8hrs
Tap A's 1 hr work = 1/12
Tap B's 1 hr work = 1/16
Tap C's 1 hr work = -1/8
Tap (A+B+C)'s 1 hr work = 1/12 + 1/16 - 1/8
= 7-6/48 = 1/48 = 48 hours
Hence, all the taps will take 48 hrs to fill the tank.
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