Question

Two taps can fill a tub in 90 mins and 45 mins, respectively. A drain can empty it in 60 mins. If all the three are kept open simultaneously for 30 mins and then the drain is closed, how long will it take for the tub to be full?​

Answer 1

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Step-by-step explanation:

TOTAL FILL TIME = 1/[ 1/5 + 1/7 - 1/3] = 105 / [21 +15 - 35] = 105 minutes.

Answer 2

Time required=${( \frac{1}{90 } + \frac{1}{60} ) - \frac{1}{60} } \times 30$

So,

$\frac{1}{90} \times 30 \\ = \frac{1}{3}$

Then, time required for filing the remaining tub by tap A and B$\frac{2}{3} \times( \frac{1}{60} + \frac{1}{90} )$

Therefore,

$\frac{2}{3} \times \frac{180}{5}$

$= \frac{2}{3} \times 36$

$= 2 \times 12$

$= 24 \: min$