Tap A can fill an empty cistern in 5 hours and tap B can empty it in 6 hours. How long will it take to fill the cistern, if both the taps ar

Question

Tap A can fill an empty cistern in 5 hours and tap B can empty it in 6 hours. How long will it take to fill the cistern, if both the taps are opened together?

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Natalia 5 days 2021-09-09T03:46:07+00:00 1 Answer 0 views 0

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    2021-09-09T03:47:13+00:00

     \huge\rm { ☆_!! Question !_! ☆}

    Tap A can fill an empty cistern in 5 hours and tap B can empty it in 6 hours. How long will it take to fill the cistern, if both the taps are opened together?

     \huge\rm { ☆_!! Answer !_! ☆}

    Time taken by tab 8 to fill the cistern = 5 hrs

    ∴ Work done by tap A in one hour = ⅕

    Time taken by to empty the cistern = 6 hrs

    ∴ Work done by tab B in one hour = -⅙

    [ ∵ tap B empties the cistern ]

    ∴ Net work done by taps A and B in 1 hour ➜

    ⅕ – ⅙ =   \tt  \frac{1}{30}

      \tt  \frac{1}{30} of the cistern is filled in 1 hour when both taps A and B are open.

    ∴when both steps A and B are open the cistern will be completely filled in 1 ÷   \tt  \frac{1}{30}

    ➜ 1 ÷   \tt  \frac{1}{30}

    ➜ 1 ×   \tt  \frac{30}{1}

    ➜ 30 hours

    hence , the cistern will get filled up in 30 hours , if both taps A and B are opened together.

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