Pipes & Cistern Questions and Answers

Answer: C

Work in rates: a pipe that fills a tank in \( n \) units of time fills \( \tfrac{1}{n} \) of it per unit, and rates add (an emptying pipe counting negative).

A is five times as fast, so A's time is a fifth of B's.

\[ B - \frac{B}{5} = 32 \quad\Longrightarrow\quad \frac{4B}{5} = 32 \]

\[ B = 40, \qquad A = 8 \text{ minutes} \]

\[ \frac{1}{8} + \frac{1}{40} = \frac{5 + 1}{40} = \frac{3}{20} \]

\[ t = \frac{20}{3} \text{ minutes} \]

Answer: B

Let the capacity of the tank be LCM(10, 30) = 30 units.
=> Efficiency of pipe A = 30 / 10 = 3 units / minute
=> Efficiency of pipe A = 30 / 30 = 1 units / minute
=> Combined efficiency of pipe A and pipe B = 4 units / minute
 
Therefore, time required to empty the tank if both pipes work = 30 / 4 = 7 minutes 30 seconds

Answer: A

Rates add when pipes work together:

\[ \frac{1}{20} + \frac{1}{30} = \frac{3 + 2}{60} = \frac{5}{60} = \frac{1}{12} \]

\[ \therefore\; \text{time} = 12 \text{ minutes} \]

The combined time must be shorter than either pipe alone, so anything of 20 minutes or more can be discarded before any arithmetic is done.

Answer: D

If A can fill a tank in x hours and B can fill a tank in y hours. Then the tank will be filled (empty) in = (xy / y-x) hours
Time taken by A = 9 hours
Time taken by B = 10 hours
Time taken by A and B = (9×10 / 10-9) = 90 hours.
 

Answer: B

Convert each to a decimal.

\[ \frac{12}{14} = 0.857, \qquad \frac{13}{19} = 0.684 \]

\[ \frac{17}{21} = 0.810, \qquad \frac{7}{8} = 0.875 \]

The smallest is \( \tfrac{13}{19} \). It is also the only one whose numerator is well below three quarters of its denominator, which is a quick way to spot it.

Answer: C

Let the fraction be x/y.

=> (x+1)/y = 1

=> x+1 = y-(1) x/(y-1) = 1/2

=> 2x = (y+1)-(2)

=>Equating (1) and (2)

=> x+1 = 2x-1

=>x=2

Substituting the value of x in (1)

=>y=3

=>2/3

Answer: D

Deal with the two stages separately. In the first 3 minutes both pipes run:

\[ 3\left(\frac{1}{12} + \frac{1}{15}\right) = 3 \times \frac{5 + 4}{60} = 3 \times \frac{9}{60} = \frac{9}{20} \]

That leaves \( 1 - \tfrac{9}{20} = \tfrac{11}{20} \) for B alone at \( \tfrac{1}{15} \) per minute:

\[ t = \frac{11/20}{1/15} = \frac{11}{20} \times 15 = \frac{33}{4} = 8\tfrac{1}{4} \text{ minutes} \]

which is 8 minutes 15 seconds, since a quarter of a minute is 15 seconds.

Answer: C

Let the slower pipe alone fill the tank in x minutes.

	1	+	3	=	1
	x		x		36

	4	=	1
	x		36

 x = 144 min.

Answer: C

Suppose pipe A alone takes x hours to fill the tank.

	1	+	2	+	4	=	1
	x		x		x		5

	7	=	1
	x		5

 x = 35 hrs.

Answer: C

When we have question like one is filling the tank and other is empting it, then we subtraction as,

Filled in 1 hour = 1/4

Empties in 1 hour = 1/9

Net filled in 1 hour = 1/4 - 1/9

= 5/36

So cistern will be filled in 36/5 hours i.e. 7.2 hours