Question

A tank can be filled by pipe A in 15 minutes and by pipe B in 10 minutes another pipe C can empty the tank in 30 minutes all three pipes are in operation simultaneously After 3 minutes pipe C is not used in how many minutes will the remaining tank be filled by pipes A and B

Answer 1

A can fill it in 15 minutes

in 1 minute, A can fill = 1/15 of the tank

B can fill it in 10 minutes

in 1 minute, B can fill = 1/10 of the tank

C can empty it in 30 minutes

in 1 minute, C can empty = 1/30 of the tank
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If all taps are opened at once for 3 minutes, portion of tank filled

= portion filled by A and B in 3 minutes - portion emptied by C in 3 minutes

$= 3 \times \frac{1}{15} + 3 \times \frac{1}{10} - 3 \times \frac{1}{30} \\ \\ = \frac{1}{5} + \frac{3}{10} - \frac{1}{10} \\ \\ = \frac{2 + 3 - 1}{10} \\ \\ = \frac{4}{10} = \frac{2}{5}$

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In first 3 minutes, 2/5 of the tank is filled.

Remaining portion = 1 - 2/5 = (5-2)/5 = 3/5

Tap C is closed. A and B will have to fill the remaining 3/5 of the tank.

in 1 minutes, Tap A and B can fill portion of

tank $= \frac{1}{15} + \frac{1}{10} = \frac{2 + 3}{30} = \frac{5}{30} = \frac{1}{6}$

Time needed to fill 3/5 of the tank =

$= \frac{3}{5} \div \frac{1}{6} = \frac{3}{5} \times \frac{6}{1} = \frac{18}{5} = 3.6 \: minutes$

So A and B will take 3.6 minutes to take fill the rest of the tank.

Answer 2

Answer:

18/5 (or) 3.6 minutes

Step-by-step explanation:

Given:

Work done by pipe A to fill the tank in 1 minute = 1/15.

Work done by pipe B in to fill the tank 1 minute = 1/10.

Work done by pipe C to empty the tank in 1 minute = 1/30.

Given that After 3 minutes pipe C is not used.

So, Amount of work done in 3 minutes:

Part filled in 3 minutes(A + B) - Part Emptied in 3 minutes

= 3 * (1/15 + 1/10) - 3(1/30)

= 5/10 - 1/10

= 4/10

= 2/5.

So in 3 minutes. (2/5) part is filled.

Remaining part = 1 - (2/5) = 3/5.

Given that Part C is closed after 3 minutes.So, Remaining part will be filled by A and B.

= 1/15 + 1/10

= 5/30

= 1/6.

So, 1/6 part is filled in 1 - minute.

Then, 3/5 th part can be filled in?

= (3/5) * 6/1

= 18/5 minutes

Therefore, time taken to fill the remaining tank = 18/5 (or) 3.6 minutes.

Hope it helps!