Pipes and cisterns-Basic test 1

Answer: Option B

Explanation

According to the formula, if a pipe empties $\frac{1}{\mathrm{x}}$ part of tank in 1 hour, then it takes x hours to fully empty the tank.

$$\begin{gathered} \frac{1}{\mathrm{x}}=\frac{1}{7} \\ \therefore \mathrm{x}=7 \end{gathered}$$

The pipe will take 7 hours to empty the tank.

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, ${{}_{}}_{}\frac{20\times 30}{20+30}=\frac{600}{50}=12 {\min }_{}$

The tank will be filled in 12 min when both the pipes are opened simultaneously.

Hence option B is correct

Answer: Option A

Explanation

According to the question, the pump takes 2.5 hours to fill the tank because of the leakage.

Normally with no leakage it takes 2 hours to fill the tank. We can say that 25% of the tank will be filled in 0.5 hours.

There is difference of 0.5 hours between filling and leaking. And the leak empties 25% of the tank in 2.5 hours

so, 100% of the tank will be empties in $\frac{100}{25}\times 2.5=4\times 2.5=10 \mathrm{hours}$

Hence option A is correct

Answer: Option D

Explanation

Let the leak take x hours to empty the tank.

Now part of the tank filled by the inlet in 1 hour is $\frac{1}{8}$

Part filled by (inlet and leak) in 1 hour= $\frac{1}{8+2}=\frac{1}{10}$

As per the question,

$\frac{1}{\mathrm{x}}=\frac{1}{8}-\frac{1}{10}=\frac{5-4}{40}=\frac{1}{40}$

x=40 hours

Hence option D is correct

Answer: Option C

Explanation

Part of the tank filled by tap in 1 hour is $\frac{1}{12}$

Part of the tank empties by leakage in 1 hour is $\frac{1}{20}$

Net part filled in 1 hour when both tap and leakage work together is

$\frac{1}{\mathrm{x}}=\frac{1}{12}-\frac{1}{20}=\frac{5-3}{60}=\frac{2}{60}=\frac{1}{30}$

 x=30 hours

 Hence option C is correct