Pipes and cisterns-Hard test 2

Answer: Option C

Explanation

Since the leak can empty the tank in 8 min,
In 1 hour, part of the tank emptied $=\frac{1}{18}$

After opening the tap
In 1 hour, part of the tank emptied $=\frac{1}{24}$

Let us consider the tap fills the tank in x hours.
So, In 1 hour, part of the tank filled by the tap$=\frac{1}{x}$

According to the question,

$\Rightarrow \frac{1}{x}-\frac{1}{18}=\frac{1}{24}$

upon cross multiplication and solving we get x = 72

Since the tap admits 6 liters of water per hour, it will admit $16\times 72=1152$ liters of water

Hence option C is correct.

Answer: Option C

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 $\left\{ \mathrm{y} \left[1-\frac{\mathrm{t}}{\mathrm{x}}\right] \right\}$ hours.

So, $\left\{ 4 \left[1-\frac{6}{12}\right] \right\}=4\times \frac{6}{12}=2 \mathrm{hours}$

Hence, the tank will be filled in 2 hours both the pipes are opened simultaneously.

Hence option C is correct.

Answer: Option C

Explanation

Let the total capacity of the tank be x liters

As per the question,

$$\begin{gathered} \frac{1\mathrm{x}}{4}=20 \\ \Rightarrow 1\mathrm{x}=20\times 4 \\ \Rightarrow \mathrm{x}=\frac{20\times 4}{1}=80\mathrm{L} \end{gathered}$$

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.

According to the question x+y+z=120

So,

 $$\begin{gathered} 120=\frac{180\times 140\times \mathrm{z}}{(180\times 140)+(140\times \mathrm{z})+(\mathrm{z}\times 180)} \\ 120=\frac{25200\mathrm{z}}{25200+140\mathrm{z}+180\mathrm{z}} \\ 120=\frac{25200\mathrm{z}}{25200+320\mathrm{z}} \end{gathered}$$

Upon cross multiplication,

$$\begin{gathered} 120\left(25200+320\mathrm{z}\right)=25200\mathrm{z} \\ 3024000+38400\mathrm{z}=25200\mathrm{z} \\ 3024000=25200\mathrm{z}-38400\mathrm{z} \\ 3024000=13200\mathrm{z} \\ \mathrm{z}=\frac{3024000}{13200} \\ \mathrm{z}=229.09 \mathrm{minutes} \end{gathered}$$

Therefore, the tank will be emptied in 229.09 minutes.

Hence option B is correct.

Answer: Option C

Explanation

 As three quantities are given, let us apply the formula

M₁H₁D₁=M₂H₂D₂

As per the question,

M₁=18 H₁=16 D₁= 25

M₂=? H₂=9 D₂=8

Apply the values to the formula,

$$\begin{gathered} 18\times 16\times 25=\mathrm{x}\times 9\times 8 \\ \mathrm{x}=\frac{18\times 16\times 25}{9\times 8}=100 \\ \mathrm{x}=100 \mathrm{pumps} \end{gathered}$$

Hence option C is correct.