Pipes and Cistern ( 21 to 25 )

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Pipes and Cistern ( 21 to 25 ):


APTITUDE QUESTIONS (PIPES AND CISTERN):

21. Two pipes X and Y can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe X is opened first, in how many hours the tank shall be full?

A)    7

B)    9

C)    5

D)    7

E)    None of these

View Answer

Answer: option (C)

Explanation:

X’s work in 1 hour = 1/6, Y’s work in 1 hour = 1/4

(X + Y)’s 2 hours work when opened alternately = ((1/6)+(1/4)) = 5/12

(X + Y)’s 4 hours work when opened alternately = 10/12 = 5/6

Remaining part = (1- (5/6)) = 1/6

Now, it’s X’s turn and 1/6 part is filled by X in 1 hour.

∴ total time taken to fill the tank = (4 + 1) = 5 hours

 

22. Three taps P, Q and R can fill a tank in 12, 15 and 20 hours respectively. If P is open all the time and Q and R are open for one hour each alternately, the tank will be full in:

A)    6 hrs

B)    7 hrs

C)    4 hrs

D)    5 hrs

E)    None of these

View Answer

Answer: option (B)

Explanation:

(X + Y)’s 1 hours work = ((1/12)+(1/15)) = 9/60 = 3/20

(X + Z)’s 1 hours work = ((1/12)+(1/20)) = 8/60 = 2/15

Part filled in 2 hrs = ((3/20)+(2/15)) = 17/60 ; Part filled in 6 hrs = (3*(17/60)) = 17/20

Remaining part = (1- (17/20)) = 3/20

Now, it is the turn of X and Y and 3/20 part is filled by X and Y in 1 hour.

∴ total time taken to fill the tank = 6 + 1 = 7 hours

 

23. Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 galons per minute. All pipes can fill the tank in 15 minutes. The capacity of the tank is:

A)    60 gallons

B)    100 gallons


C)    120 gallons

D)    180 gallons

E)    None of these

View Answer

Answer: option (C)

Explanation:

Work done by the waste pipe in 1 minute = ((1/15) – (1/20)+(1/24)) = ((1/15)-11/120)) = -1/40

∴ Volume of 1/40 part = 3 gallons

Volume of whole = (3*40) = 120 gallons

 

24. Two pipes X and Y can fill a cistern in 37(1/2) minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe Y is turned off after:

A)    8 min

B)    9 min

C)    10 min

D)    15 min

E)    None of these

View Answer

Answer: option (B)

Explanation:

Let Y be turned off after x minutes.

Then, part filled by (X + Y) in x min + Part filled by X in (30 – x) min = 1

∴ x((2/75)+(1/45)) + (30 – x) * (2/75) = 1

<=> 11x/225  +  (60-2x)/75 = 1 <=> 11x + 180 – 6x = 225 <=> x = 9

 

25. Three pipes X, Y and Z can fill a tank in 6 hours. After working for 2 hours together, Z is closed and X and Y can fill the remaining part in 7 hours. The number of hours taken by Z alone to fill the tank is:

A)    20

B)    13

C)    14

D)    16

E)    None of these

View Answer

Answer: option (C)

Explanation:

Some part filled in 2 hours = 2/6 = 1/3, Remaining part = (1- (1/3)) = 2/3

∴ (X + Y)’s 7 hours work = 2/3; (X + Y)’s 1 hours work = 2/21

∴ Z’s 1 hour work = [(X + Y + Z)’s 1 hour work – (X + Y)’s 1 hour work] = ((1/6)-(2/21)) = 1/14

∴ Z alone can fill the tank in 14 hours

 

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