BEST APTITUDE QUESTIONS ON PIPES AND CISTERNS

This Test is based on the  of  pipes and cisterns concepts oriented aptitude problems with solutions which contain cistern overflow pipe which sometimes filled or leaked by two or more pipes.
It also contains the shortcuts and formulas to solve the problems

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 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank (in litres) is

A. 5880 litres                                         B.5670 litres

C. 5950 litres                                         D.5760 litres

ANSWER & EXPLANATION

ANSWER:D
Explanation: Work done by the inlet in 1 hour = 16−18=124
Work done by inlet in 1 min=124∗160=11440=>Volume of 1/1440 part = 4 liters
Volume of whole = (1440 * 4) litres = 5760 litres.

2. An pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 (1/2)hours to fill the tank. If the tank is full, how much time will the leak take to empty it ?

A.21 hours                                                  B. 20 hours

C. 30 hours                                                 D. 40 hours

ANSWER & EXPLANATION

ANSWER:A
Work done by the leak in 1 hour = [13−1(72)]=13−27=121
The leak will empty the tank in 21 hours

3.Three pipes X, Y and Z can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. X, Y and Z discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?

A. 611                                                B.511

C. 711                                                D. 811

ANSWER & EXPLANATION

ANSWER: A
Part of the tank filled by pipe X in 1 minute = 1⁄30
Part of the tank filled by pipe Y in 1 minute = 1⁄20
Part of the tank filled by pipe Z in 1 minute = 1⁄10
Here we have to find the proportion of the solution R.
Pipe Z discharges chemical solution R
Part of the tank filled by pipe Z in 3 minutes = 3×110=310
Part of the tank filled by pipe X,Y and Z together in 1 minute =
130+120+110=1160Part of the tank filled by pipe X,Y and Z together in 3 minute = 3×1160=1120
Required proportion = (310)(1120)=(3×20)(10×11)=611

4. 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:

A. 81 min.                                                   B. 108 min.

C. 144 min.                                                 D. 192 min.

ANSWER & EXPLANATION

ANSWER: C
Let the slower pipe alone fill the tank in x minutes.
Then, faster pipe will fill it in x/3 minutes.
1/x + 3/x = 1/x
4/x = 1/36
x = 144 min.

5.Two pipes can till a tank in 10 hours and 12 hours respectively while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time will the tank be filled ?

A. 7hrs 30 min                                              B. 7hrs 40 min

C. 9hrs 50 min                                              D.8hrs 40 min

ANSWER & EXPLANATION

ANSWER: A
Net part filled in 1 hour = (110+112−120)= 860 = 215
The tank will be full in 15/2 hrs 7 hrs 30 min

6. Two pipes X and Y can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, Pipe X is turned off. What is the total time required to fill the tank ?

A. 10 min 20 sec                                                   B.10 min 10 sec

C. 10 mi n 30 sec                                                  D. 10 min 40 sec

ANSWER & EXPLANATION

ANSWER: D
Part of tank filled by X + Y in 1 minute = ( 1 / 15 + 1 / 20 )
So tank filled by X + Y in 4 minute = 4 ( 1 / 15 + 1 / 20 ) = 7 / 15
Part remaning = 1 - ( 7 / 15 ) = 8 / 15
1 / 20 part is filled by Y in 1 minute
So, 8 / 15 part will be filled in = ( 20 / 1 )* ( 8 / 15 ) = 32 / 3 = 10 minutes 40 sec.

7 . A leak in the bottom of a tank can empty the full tank in 6 hrs. An inlet pipe fills water at the rate of 4 lit. a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hrs. The capacity of the tank in litres is :

A. 5,260                                                               B.5,760

C. 6,970                                                                D. 5,846

ANSWER & EXPLANATION

ANSWER :B
Work done by the inlet in 1 hr. = (16−18)=1/24
Work done by the inlet in 1 min. = (124×160)=11,440
Volume of 11,440 part = 4 litres.
Whole volume = (1,440×4)=5,760 litres.

8. A leak in the lower portion of a tank can empty the full tank in 9 hrs. An inlet pipe fills water at the rtae of 10 lit. a minute. When the tank is full, the inlet is opened and due to leak, the tank is empty in 16 hrs. How many litres does the cistern hold ?

A. 15,580                                                    B. 16,960

C. 12,342                                                    D. 18,200

ANSWER & EXPLANATION

ANSWER: C
Work done by the inlet in 1 hr = 19−116=7144
Work done by the inlet in 1 min. = (7144×160)=78,640
Volume of 78,640 part = 10 litres.
Whole volume = 10×8,640/7=12,342 litres

9.Two pipes X and Y can fill a tank in 15 minutes and 40 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe X is turned off. What is the total time required to fill the tank?

A. 10 min 10 sec                                                   B. 25 min 20 sec

C. 29 min 20 sec                                                   D.20 min 10 sec

ANSWER & EXPLANATION

ANSWER: C
Part filled by pipe X in 1 minute= 115
Part filled by pipe Y in 1 minute= 140
Part filled by pipe X and pipe Y in 1 minute= 115+140=11120
pipe X and pipe Y were open for 4 minutes.
Part filled by pipe X and pipe Y in these 4 minutes = 4×11120=1130Remaining
part to be filled = 1−1130=1930
Time taken by pipe Y to fill this remaining part = (1930)
(140)=19×4030=19×43=763=2513 minutes = 25 minutes 20 seconds
Therefore, total time required = 4 minutes + (25 minutes 20 seconds) = 29 minutes 20 seconds

10. Pipes X and Y can fill a tank in 5 hours and 6 hours respectively. Pipe Z can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in.

A.395                                                   B. 3917

C. 375                                                  D. 3717

ANSWER & EXPLANATION

ANSWER: B
Net part filled in 1 hour =
(15+16−112)=1760hrs=3917

11. 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.90 gallons                                                   B. 80 gallons

C. 120 gallons                                                D. 190 gallons

ANSWER & EXPLANATION

ANSWER: C
Work done by the waste pipe in 1 minute = 1/15 - ( 1/20 + 1/24)
= 1/15 - 11/120
= - 1/40 . [-ve sign means emptying]
Volume of 1/40 part = 3 gallons.
Volume of whole = (3 x 40) gallons = 120 gallons.