Pipes and cisterns-Basic test 2

Answer: Option D

Explanation

According to the above given formula, If pipe A  and B fills a tank in x and y hours respectively, but a third pipe C empties the full tank in z hours then the net portion filled in 1 hour when all of them are opened together is $\frac{\mathrm{xyz}}{\mathrm{yz}+\mathrm{xz}-\mathrm{xy}}$ hours.

So,

 $$\begin{gathered} \frac{3\times 4\times 2}{(4\times 2)+(3\times 2)-(3\times 4)} \\ =\frac{24}{2}=12 \mathrm{hours} \end{gathered}$$

Therefore, the tank will be filled in 12 hours when all the pipes are opened simultaneously.

Hence option D is correct

Answer: Option A

Explanation

According to the above given formula, If pipe A  and B fills a tank in x and y hours respectively, but a third pipe C empties the full tank in z hours then the net portion filled in 1 hour when all of them are opened together is $\frac{\mathrm{xyz}}{\mathrm{yz}+\mathrm{xz}+\mathrm{xy}}$ hours.

So,

 $$\begin{gathered} \frac{4\times 5\times 10}{(4\times 5)+(4\times 10)+(5\times 10)} \\ =\frac{20}{11}=1\frac{9}{11} \mathrm{hours} \end{gathered}$$

Therefore, the tank will be filled in $1\frac{9}{11}$ hours when all the pipes are opened simultaneously.

Hence, option A is correct.

Answer: Option B

Explanation

According to the above given formula, If pipe A  and B fills a tank in x and y hours respectively, but a third pipe C empties the full tank in z hours then the net portion filled in 1 hour when all of them are opened together is $\frac{\mathrm{xyz}}{\mathrm{yz}+\mathrm{xz}-\mathrm{xy}}$ hours.

According to the question x+y+z=10

So,

 $$\begin{gathered} 5=\frac{20\times 10\times \mathrm{z}}{(20\times 10)+(10\times \mathrm{z})+(\mathrm{z}\times 20)} \\ 5=\frac{200\mathrm{z}}{200+10\mathrm{z}+20\mathrm{z}} \\ 5=\frac{200\mathrm{z}}{200+30\mathrm{z}} \end{gathered}$$

Upon cross multiplication,

$$\begin{gathered} 5\left(200+30\mathrm{z}\right)=200\mathrm{z} \\ 1000+150\mathrm{z}=200\mathrm{z} \\ 1000=200\mathrm{z}-150\mathrm{z} \\ 1000=50\mathrm{z} \\ \mathrm{z}=\frac{1000}{50} \\ \mathrm{z}=20 \mathrm{minutes} \end{gathered}$$

Therefore, the tank will be emptied in 20 minutes.

Hence option B is correct

Answer: Option C

Explanation

According to the above given formula, if pipe A can comletely fill a tank in x hours and pipe B can empty the same tank in y hours, then the time taken to fill the tank when both the pipes are opened simultaneously is  $\frac{\mathrm{xy}}{\mathrm{x}-\mathrm{y}}$ hours.

So, $\frac{5\times 4}{5-4}=\frac{20}{1}=20 \mathrm{hours}$

Therefore, the tank will be filled in 20 hours when both the pipes are opened simultaneously.

Hence option C is correct.

Answer: Option A

Explanation

According to the above given formula, if pipe A can comletely fill a tank in x hours and pipe B can empty the same tank in y hours, then the time taken to fill the tank when both the pipes are opened simultaneously is  $\frac{\mathrm{xy}}{\mathrm{x}-\mathrm{y}}$ hours.

So, $\frac{60\times 30}{60-(-30)}=\frac{1800}{90}=20 \mathrm{minutes}$

Therefore, the tank will be filled in 20 minutes when both the pipes are opened simultaneously.

Hence option A is correct.