Pipes and cisterns-Basic test 2

Answer: Option D

Explanation

According to the formula, If Two pipes A and B can fill the tank in x and y min respectively. If both pipes are opened together, then the time after which pipe B should be closed so that the tank is full in t min is $\left\{ \mathrm{y} \left[1-\frac{\mathrm{t}}{\mathrm{x}}\right] \right\}$ min.

So, $\left\{ 60 \left[1-\frac{3}{10}\right] \right\}=60\times \frac{3}{10}=18 \min$

The tank will be filled in 18 min both the pipes are opened simultaneously.

Hence option D is correct.

Answer: Option C

Explanation

According to the 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 $\frac{\mathrm{xyz}}{\mathrm{xy}+\mathrm{yz}+\mathrm{zx}}$hours.

So,

 $$\begin{gathered} \frac{4\times 5\times 10}{(4\times 5)+(5\times 10)+(4\times 10)} \\ =\frac{200}{110}=\frac{20}{11} \mathrm{or} 1\frac{9}{11}\mathrm{hours} \end{gathered}$$

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

Hence option C is correct

Answer: Option A

Explanation

According to the 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, $\frac{15\times 20}{20-15}=\frac{300}{5}=60 \mathrm{hours}$

The tank will be filled in 60 hours when both the pipes are opened simultaneously.

Hence option A is correct

Answer: Option C

Explanation

According to the 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 $\frac{\mathrm{xyz}}{\mathrm{xy}+\mathrm{yz}+\mathrm{zx}}$hours.

So,

 $$\begin{gathered} \frac{8\times 6\times 20}{(8\times 6)+(8\times 20)+(6\times 20)} \\ =\frac{960}{328}=\frac{120}{41} \mathrm{or} 2\frac{38}{41}\mathrm{hours} \end{gathered}$$

The tank will be filled in $2\frac{38}{41}$ hours when all the pipes are opened simultaneously.

Hence option C is correct

Answer: Option D

Explanation

According to the 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, $\frac{45\times 120}{120-45}=\frac{5400}{75}=72 \mathrm{minutes}$

The tank will be filled in 72 minutes when both the pipes are opened simultaneously.

Hence option D is correct