Quantitative Aptitude Quiz for UPSI: 06 April 2021

1. A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?

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a) 5260 liters
b) 5760 liters
c) 5846 liters
d) 6970 liters

Explanation:
1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760

2. Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?

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a) 7 min
b) 8 min
c) 9 min
d) 10 min
 

Explanation:

1/10 + 1/15 = 1/6 * 4 = 2/3

1 - 2/3 = 1/3

1/10 + 1/15 - 1/x = 1/3

x = 8

3. An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?

a) 4/9
b) 2/3
c) 4/7
d) 1/6

Explanation:

2/3 ---- 12

x ----- 8 ==> 4/9

4. Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?

a) 18 hrs
b) 16 hrs
c) 15 hrs
d) 12 hrs

Explanation:

1/20 + 1/30 = 1/12

1 + 1/3 = 4/3

1 --- 12

4/3 --- x

4/3 * 12 = 16 hrs

5. Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?

a) 25 hrs
b) 28 hrs
c) 20 hrs
d) 35 hrs
 

Explanation:

1/x + 1/(x + 10) = 1/12

x = 20

6. pipes P and Q would fill a cistern 18 and 24 minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the cistern may be just filled in 12 minutes?

a) after 12 mins
b) after 9 mins
c) after 8 1/2 mins
d) after 10 mins
 

Explanation:

x/18 + 12/24 = 1

x = 9

7. A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?

a) 45 hrs
b) 60 hrs
c) 75 hrs
d) 90 hrs

Explanation:

1/9 - 1/x = 1/10

=> 90 hrs

8. A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 28 minutes. When both pipes are opened, find when the cistern will be full?

a) 60 min
b) 80 min
c) 70 min
 d) 48 min
 

Explanation:

1/20 - 1/28 = 1/70

70 minutes

9. Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?

a) 6 min
b) 12 min
c) 19 min
d) 10 min
 

Explanation:

1/8 + 1/24 = 1/6

6 * 2 = 12

10. A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?

a) 3 PM
b) 7 PM
c) 4 PM
d) 5 PM

Explanation:

1 to 2 = 1/4
2 to 3 = 1/4 + 1/5 = 9/20
 After 3 AM = 1/4 + 1/5 - 1/2 = -1/20
 1/4 + 9/20 = 14/20
 1 h ---- 1/20
 x ----- 14/20

 14 hours ==> 5 PM