Math, asked by mathuratrika2020, 6 months ago

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

Answered by minimr1977
3

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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