Pipes and cisterns-Basic test 2

Answer: Option A

Explanation

According to the 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, $\frac{18\times 12}{12+18}=\frac{216}{30}=\frac{36}{5}=7\frac{1}{5} \mathrm{hours}$

When both the pipes are opened simultaneously. tank will be filled in $7\frac{1}{5}$ hours

Hence option A is correct

Answer: Option B

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 $\frac{\mathrm{xyz}}{\mathrm{yz}+\mathrm{xz}-\mathrm{xy}}$ hours.

So,

 $$\begin{gathered} \frac{10\times 16\times 32}{(10\times 32)+(16\times 32)-(10\times 16)} \\ =\frac{5120}{672}=\frac{160}{21} \mathrm{or} 7\frac{13}{21}\mathrm{hours} \end{gathered}$$

The tank will be filled in $7\frac{13}{21}$ hours when all the pipes are opened simultaneously.

Hence option B is correct

Answer: Option B

Explanation

According to the 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, $\frac{2\times 3}{2+3}=\frac{6}{5}=1.2 \mathrm{hours}$

The tank will be filled by both the pipe when opened simultaneously in 1.2 hours

Hence option B is correct.

Answer: Option C

Explanation

According to the 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, $\frac{10\times 15}{15-10}=\frac{150}{5}=30 \mathrm{minutes}$

The tank will be filled by both the pipe when opened simultaneously in 30 minutes.

Hence, option C 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.

So,

 $$\begin{gathered} \frac{3\times 4\times 5}{(4\times 5)+(3\times 5)-(3\times 4)} \\ =\frac{60}{23} \mathrm{or} 2\frac{14}{23}\mathrm{hours} \end{gathered}$$

Therefore, the tank will be filled in $2\frac{14}{23}$ hours when all the pipes are opened simultaneously.

Hence option B is correct.