Quant Quiz

Q1)-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?

20 hours

25 hours

35 hours

Cannot be determined

Ans.- C
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 hours

Q2)-One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:

180 min

144 min

126 min

114 min

Ans.- A
The faster pipe is equivalent to 4 slower pipes together.
5 slower pipes together can fill the tank in 36 minutes.
Therefore, 1 slower pipe can fill the tank in 36×5=180 minutes.

Q3)-Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

12 min

14 min

15 min

18 min

Ans.- A
Part filled by A in 1 min = 1/20
Part filled by B in 1 min =1/30
Part filled by (A + B) in 1 min = (1/20 + 1/30 )=1/12
Both pipes can fill the tank in 12 minutes.

Q4)-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 a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 24 hours. How many liters does the tank hold?

4010 litre

2220 litre

1920 litre

2020 litre

Ans.- C
water filled by the inlet pipe in 24 hours = water emptied by the leak in 24−6=18 hours.
Therefore, water emptied by the leak in 6 hours = water filled by the inlet pipe in 8 hours
i.e., capacity of the tank
= water filled by the inlet pipe in 8 hours
=8×60×4=1920 litre.

Q5)-A cistern can be filled by a tap in 12 hours and by the other tap in 9 hours. If both taps are opened together how long will it take to fill the cistern?

6/7 hours

36/7 hours

7/36 hours

None of these

Ans.- B
Time taken by the 1st tap to fill the cistern = 12 hours
Therefore, work done by the 1 st tap in 1 hour = 1/12
Time taken by the 2nd tap to fill the cistern = 9 hours.
Therefore, work done by the 2nd tap in 1 hour = 1/9
Therefore, work done by the both taps in 1 hour = 1/12 + 1/9
= (3 + 4)/36
= 7/36
Therefore, both taps will fill the cistern in = 36/7 hours.

Q6)-A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?

480 liters

600 liters

720 liters

800 liters

Ans.- A
1/x - 1/20 = -1/24
x = 120
120 x 4 = 480

Q7)-One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in

144 mins

140 mins

136 mins

132 mins

Ans.- A
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute = 1/x + 3/x =1/36
4/x= 1/36
x = 144 mins

Q8)-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?

25 hrs

28 hrs

20 hrs

35 hrs

Ans.- C
1/x + 1/(x + 10) = 1/12
x = 20

Q9)-A cistern can be filled in 9 hours but due to a leak at its bottom it takes 10 hours. If the cistern is full, then the time that the leak will take to make it empty will be ?

20 hours

19 hours

90 hours

80 hours

Ans.- C
Part filled without leak in 1 hour = 1/9
Part filled with leak in 1 hour = 1/10
Work done by leak in 1 hour = (1/9) - (1/10) = 1/ 90
We used subtraction as it is getting empty. So total time to empty the cistern is 90 hours

Q10)-A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water at the rate of 6 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many liters does the cistern hold?

7580

7960

8290

8640

Ans.- D
Work done by the inlet in 1 hour = 1/8 - 1/12 = 1/24
Work done by the inlet in 1 min. = 1/24 x 1/60 = 1/1440
Given, volume of 1/1440 part = 6 liters.
⇒ Volume of whole = 6 * 1440 = 8640 liters.