Pipes and cisterns-Hard test 1

Answer: Option C

Explanation

In one minute, 9 taps fill $\frac{1}{20}$^th part of water tank

similarly, in one minute, 1 tap fills $\frac{1}{20\times 9}=\frac{1}{180}$^th part of water tank

Let the number of taps used to fill the tnk in 15 min be x.

So, $\mathrm{x} \times \frac{1}{180}=\frac{1}{15}$

upon cross multiplication,

$\mathrm{x}=\frac{180}{15}=12 \mathrm{taps}$

Therefore, 12 taps can fill the tank in 15 minutes

Hence option C is correct.

Answer: Option B

Explanation

Now as one pipe fills the cistern and other empties it, 

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.

$\frac{5\times 8}{8-5}=\frac{40}{3}$

Since $\frac{40}{3}$^rd part is emptied in 1 hour.

And $\frac{3}{4}$th part will be empties in

$\frac{40}{3}\times \frac{3}{4}=10 \mathrm{hours}$

Hence option B is correct.

Answer: Option C

Explanation

Let the total capacity of the tank be x liters

As per the question,

$$\begin{gathered} \frac{3\mathrm{x}}{4}=30 \\ \Rightarrow 3\mathrm{x}=30\times 4 \\ \Rightarrow \mathrm{x}=\frac{30\times 4}{3}=40\mathrm{L} \end{gathered}$$

Hence option C is correct.

Answer: Option C

Explanation

 As three quantities are given, let us apply the formula

M₁H₁D₁=M₂H₂D₂

As per the question,

M₁=12 H₁=6 D₁= 15

M₂=? H₂=9 D₂=12

Apply the values to the formula,

$$\begin{gathered} 12\times 6\times 15=\mathrm{x}\times 9\times 12 \\ \mathrm{x}=\frac{12\times 6\times 15}{9\times 12} \\ \mathrm{x}=2\times 5 \\ \mathrm{x}=10 \mathrm{pumps} \end{gathered}$$

Hence option C is correct.

Answer: Option C

Explanation

Time taken by all tohethet to fill the tank is 15 minutes

Let the capacity of the tank be x gallons

Quantity of water filled in the tank in 1 min when all the pipes A, B and C are opened simultaneously,

$$\begin{gathered} =\frac{\mathrm{x}}{20}+\frac{\mathrm{x}}{24}-3=\frac{\mathrm{x}}{15} \\ \Rightarrow \frac{{\displaystyle \mathrm{x}}}{{\displaystyle 20}}+\frac{{\displaystyle \mathrm{x}}}{{\displaystyle 24}}-\frac{{\displaystyle \mathrm{x}}}{{\displaystyle 15}}=3 \\ \Rightarrow \frac{{\displaystyle 6\mathrm{x}+5\mathrm{x}-8\mathrm{x}}}{{\displaystyle 120}}=3 \\ \Rightarrow 3\mathrm{x}=3\times 120 \\ \Rightarrow \mathrm{x}=\frac{3\times 120}{3}=120 \mathrm{gallons} \end{gathered}$$

Hence option C is correct.