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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Answer 1

$\huge\rm { ☆_!! Question !_! ☆}$

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.