Pipes & Cistern Questions and Answers

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

Answer: D

We are given that A fills the pool at the rate of 4 liters every 3 minutes and B fills the pool at the rate of 3 liters every 4 minutes.
=> Pool filled by A in 12 minutes = 4 x 4 = 16 liters
=> Pool filled by B in 12 minutes = 3 x 3 = 9 liters
=> Pool filled in 12 minutes = 16 + 9 = 25 liters

or we can say to fill 25 liters water, they will take 12 minutes.
Therefore to fill 1000 liters they will take (12*1000)/25 minutes i.e. 8 hours.
=> Since they will put a bucket at the same instant every 12 minutes. (LCM of 3 and 4 minutes = 12 minutes).
=> After every 12 minutes they will take rest for 3 minutes.
=> Overall  (8*60)/12 i.e 40 times they take rest while working .
=> So every 12 minutes should be considered 15 (12+3) minutes for 40 times.
=> But after having taken 39 times . The pool of capacity 1000 liters will be filled.
=> Last 3 minutes must not be considered.

Therefore, to fill 1000 liters (25 x 40 liters), it would take (12*1000)/25 minutes i.e. 8 hours. + (39*3) minutes = 8 hrs. + 117 minutes
So ans is  9 hrs 57 minutes.

Answer: A

Lets suppose tank got filled by first pipe in X hours,

So, second pipe will fill the tank in X + 10 hours.