Pipes and cisterns-Basic test 1

Answer: Option B

Explanation

Part of the tank filled by Pipe A in 1 hour is $\frac{1}{5}$

Part of the tank filled by Pipe B in 1 hour is $\frac{1}{6}$

Part of the tank filled by pipe C in 1 hour is $\frac{1}{30}$

Net part filled in 1 hour when all pipes are opened together $\frac{1}{5}+\frac{1}{6}+\frac{1}{30}$

$=\frac{6+5+1}{30}=\frac{12}{30}=\frac{2}{5}$

Required time $=\frac{5}{2}=2\frac{1}{2} \mathrm{hours}$

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

so, $\frac{10\times 15}{10+15}=\frac{150}{25}=6 \mathrm{hours}$ 

Both the pipes together can fill the tank in 6 hours.

Hence option A 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 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, $\frac{8\times 16}{16-8}=\frac{128}{8}=16 \mathrm{hours}$ 

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

Hence option C 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 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, $\frac{2\times 3}{3-2}=\frac{6}{1}=6 \mathrm{hour}$ 

Therefore, the cistern will be filled in 6 hours when both the pipes are opened simultaneously.

Hence option B is correct

Answer: Option A

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,

 $$\begin{gathered} \frac{4\times 6\times 8}{(4\times 8)+(6\times 8)-(4\times 6)} \\ =\frac{4\times 6\times 8}{56}=\frac{24}{7} \mathrm{or} 3\frac{3}{7}\mathrm{hours} \end{gathered}$$

Therefore, the tank will be filled in $3\frac{3}{7}$ hours when all the pipes are opened simultaneously.

Hence option A is correct.