Prev Next
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