NTT Data Pipes and Cisterns Quiz – 1

Net part filled in 1 hour  is \frac{1}{4} + \frac{1}{8} - \frac{1}{10}

= \frac{10+5-4}{40}

\frac{11}{40}

Therefore The tank will be full in \frac{40}{11} hours

Work done by the leak in 1 hour =  \frac{1}{3} - \frac{2}{7}

= \frac{1}{21}

Leak will empty the tank in 21 hours

Let Q be turned off after x minutes. Then,

Part filled by (P + Q) in x min. + Part filled by P in (30 -x) min. = 1.

(x)(\frac{1}{36}+ \frac{1}{45} )+ (30 - x)\frac{1}{36} = 1

(x)(\frac{5 + 4}{180} )+ (30 - x)\frac{1}{36} = 1

\frac{x}{20} + (30 - x)\frac{1}{36} = 1

\frac{9x + 5(30 - x)}{180} = 1

\frac{4x + 150 }{180} = 1

4x + 150 = 180

4x = 30

X = 7.5

Suppose, the first pipe alone takes x hours to fill the tank.

Then, the second and third pipes will take (x - 4) and (x - 7) hours respectively to fill the tank.

\frac{1}{x} + \frac{1}{x - 4} = \frac{1}{x - 7}

(2x - 4)(x - 7) = x(x - 4)

x2 - 14x + 28 = 0

X = 11.58 or 2.42 ( neglecting 2.42 )

Work done by the waste pipe in 1 minute =

- ( \frac{1}{15} + \frac{1}{20} )

= \frac{1}{12} - \frac{7}{60}

= \frac{5 - 7}{60}

= - \frac{1}{30} (-ve sign means emptying)

Volume of \frac{1}{30} part = 5 gallon

Whole part = 30 x 5 = 150 gallon

Let the cistern be filled by pipe P alone in x hours.

Then, pipe Q will fill it in (x + 7) hours.

\frac{1}{x} + \frac{1}{x + 7} = \frac{1}{5}

5( 2x + 7 ) = x ( x + 7 )

10x + 35 = x^2 + 7x

x^2 - 3x - 35 = 0

X = 7.6

 

Part filled by P in 1 min = \frac{1}{30}

Part filled by Q in 1 min =\frac{1}{40}

Part filled by (P + Q) in 1 min = \frac{1}{30} + \frac{1}{40}

= \frac{7}{120}

Therefore both pipes can fill the tank in  \frac{120}{7}  minutes

Part filled in 5 minutes = 5 ( \frac{1}{10} + \frac{1}{15} )

= \frac{5}{6}

Remaining part = 1 - \frac{5}{6}

= \frac{1}{6}

Part filled by Q in 1 minute = \frac{1}{15}

\frac{1}{15} :  \frac{1}{6} :: 1 : x

X =  \frac{1}{6} x 15

X =  \frac{5}{2}

= 2.5 Min

Total time required = 4 + 2.5 Min = 7.5 Min

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

Faster pipe can fill the tank in \frac{x}{2}

\frac{1}{x}  + \frac{2}{x} = \frac{1}{40}

X = 120 Mins

Part of the tank filled by pipe ( A + B) in 1 min =

\frac{1}{50} + \frac{1}{30} = \frac{4}{75}

Suppose the tank is filled in x minutes.

\frac{x}{2}( \frac{4}{75} + \frac{1}{30}) = 1

\frac{x}{2}( \frac{13}{150} = 1

X = \frac{300}{13}

X = 23 Min ( Aprox)