Pipes & Cisterns Mcqs - Set 2

1)   Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together 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
Answer  Explanation 

ANSWER: 120 gallons

Explanation:
Work done by the waste pipe in 1 minute = 1/15 – (1/20 + 1/24) = – 1/40

Volume of 1/40 part = 3 gallons
Volume of whole = 3 * 40 = 120 gallons.

2)   Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full is_______?

a. 6 hrs
b. 6 2/3 hrs
c. 7 hrs
d. 7 1/2 hrs
Answer  Explanation 

ANSWER: 7 hrs

Explanation:
(A + B)’s 1 hour work = (1/12 + 1/15) = 3/20

(A + C)’s 1 hour work = (1/12 + 1/20) = 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 A and B and 3/20 part is filled by A and B in 1 hour.
Total time taken to fill the tank = (6 + 1) = 7 hrs.

3)   A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?

a. 15 min
b. 20 min
c. 27.5 min
d. 30 min
Answer  Explanation 

ANSWER: 30 min

Explanation:
Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24

Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
x/2 * 1/15 = 1 => x = 30 min.

4)   Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?

a. 10 min 20 sec
b. 11 min 45 sec
c. 12 min 30 sec
d. 14 min 40 sec
Answer  Explanation 

ANSWER: 14 min 40 sec

Explanation:
Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15

Remaining part = 1 – 7/15 = 8/15
Part filled by B in 1 minute = 1/20
1/20 : 8/15 :: 1 ; x
x = 8/15 * 1 * 20 = 10 2/3 min = 10 min 40 sec.
The tank will be full in (4 min. + 10 min. 40 sec) = 14 min 40 sec.

5)   A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?

a. 6 hrs
b. 10 hrs
c. 15 hrs
d. 30 hrs
Answer  Explanation 

ANSWER: 15 hrs

Explanation:
Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x – 5) and (x – 9) hours respectively to fill the tank.

1/x + 1/(x – 5) = 1/(x – 9)
(2x – 5)(x – 9) = x(x – 5)
x2 – 18x + 45 = 0
(x- 15)(x – 3) = 0 => x = 15

6)   A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

a. 20 hrs
b. 25 hrs
c. 35 hrs
d. Cannot be determined
Answer  Explanation 

ANSWER: 35 hrs

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

Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/5
7/x = 1/5 => x = 35 hrs.

7)   One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?

a. 81 min
b. 108 min
c. 144 min
d. 192 min
Answer  Explanation 

ANSWER: 144 min

Explanation:
Let the slower pipe alone fill the tank in x min.

Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/36
4/x = 1/36 => x = 144 min.

8)   Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill cistern. How much time will be taken by A to fill the cistern separately?

a. 1 hr
b. 2 hrs
c. 6 hrs
d. 8 hrs
Answer  Explanation 

ANSWER: 6 hrs

Explanation:
Let the cistern be filled by pipe A alone in x hours.

Then, pipe B will fill it in (x + 6) hours.
1/x + 1/(x + 6) = 1/4
x2 – 2x – 24 = 0
(x – 6)(x + 4) = 0 => x = 6.

9)   A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in?

a. 4 1/3 hrs
b. 7 hrs
c. 8 hrs
d. 14 hrs
Answer  Explanation 

ANSWER: 14 hrs

Explanation:
Work done by the tank in 1 hour = (1/2 – 1/3) = 1/14 Leak will empty the tank in 14 hrs.

10)   Two pipes A and B can separately fill a cistern in 60 min and 75 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min. In how much time, the third pipe alone can empty the cistern?

a. 90 min
b. 100 min
c. 110 min
d. 120 min
Answer  Explanation 

ANSWER: 100 min

Explanation:
Work done by the third pipe in 1 min = 1/50 – (1/60 + 1/75) = – 1/100.

[-ve sign means emptying]
The third pipe alone can empty the cistern in 100 min.

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