Pipes and cisterns-Basic test 2

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 comletely fill a tank in y hours, then the time taken by both pipes together to fill the tank is $\frac{\mathrm{xy}}{\mathrm{x}-\mathrm{y}}$ hours.

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

Therefore, the tank will be filled by both the pipe when opened simultaneously in 20 minutes.

Hence option C is correct.

Answer: Option D

Explanation

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

So, $\frac{40\times 60}{60-40}=\frac{240}{20}=120 \mathrm{minutes}$

Therefore, the tank will be filled by both the pipe when opened simultaneously in 120 minutes.

Hence option D 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,

 $$\begin{gathered} 10=\frac{30\times 40\times \mathrm{z}}{(30\times 40)+(40\times \mathrm{z})+(\mathrm{z}\times 30)} \\ 10=\frac{1200\mathrm{z}}{1200+30\mathrm{z}+40\mathrm{z}} \\ 10=\frac{1200\mathrm{z}}{1200+70\mathrm{z}} \end{gathered}$$

Upon cross multiplication,

$$\begin{gathered} 10\left(1200+70\mathrm{z}\right)=1200\mathrm{z} \\ 12000+700\mathrm{z}=1200\mathrm{z} \\ 12000=1200\mathrm{z}-700\mathrm{z} \\ 12000=500\mathrm{z} \\ \mathrm{z}=\frac{12000}{500} \\ \mathrm{z}=24 \mathrm{minutes} \end{gathered}$$

Therefore, the tank will be emptied in 24 minutes.

Hence option B is correct.

Answer: Option B

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 $\frac{\mathrm{xy}}{\mathrm{y}+\mathrm{x}}$ hours.

so, $\frac{20\times 30}{20+30}=\frac{600}{50}=12 \mathrm{minutes}$

Therefore, the tank will be filled in 12 minutes when both the pipes are opened simultaneously.

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 comletely fill a tank in y hours, then the time taken by both pipes together to fill the tank is $\frac{\mathrm{xy}}{\mathrm{x}-\mathrm{y}}$ hours.

So, $\frac{8\times 16}{16-8}=\frac{128}{8}=16 \mathrm{hours}$

Therefore, the tank will be filled in 16 hours when both the pipe are opened simultaneously.

Hence option C is correct.