# Pipes and Cistern

1.  Pipe A can fill a tank in 2hr, pipe B in 4 hrs and pipe C in 6 hrs. If all the pipes are open, in how many hours the tank will fill?

(a)

(b)

(c)

(d)

Explanation:

Part filled by A in 1 hr

Part filled by B in 1 hr

Part filled by C in 1 hr

Part filled by A+B+C in 1 hr

All the pipes together will fill the tank in hours.

2.  Tap A can fill a water tank in 25 min, tap B can fill the same tank in 40 min and tap C can empty that tank in 30 min. If all the three taps are opened together, in how many min will the tank be completely filled up or emptied? (Bank PO 2001)

(a)

(b)

(c)

(d)

Explanation:

Part filled by A+B+C in 1 hr

The tank will be full in

3. Two pipes A and B can fill a tank in 16 hours and 24 hours respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 hours?

(a) 2 hrs

(b) 4 hrs

(c) 8 hrs

(d) 16 hrs

Explanation:

Let B closed after x hours. Then,

Part filled by (A+B) in x hours

Part filled by A in (18-x) hours

Part filled by (A+B) in x hours + Part filled by A in (18-x) hours = 1

5x+54-3x-48 = 0

2x-16 = 0

x = 8 hours.

Hence, B must be closed after 8 hours.

4. Two pipes A and B can fill a cistern in 12 mins and 15 mins respectively, but a third pipe C can empty the full tank in 6 mins. A and B are kept open for 5 min in the beginning and then C is also opened. In what time is the cistern emptied? (Bank PO 2000)

(a) 30 mins

(b) 33 mins

(c) 37. 5 mins

(d) 45 mins

Explanation:

Work done by A in 1 min

Work done by B in 1 min  and

Work done by C in 1 min

Therefore, work done in first 5 min

Now, C is also opened.

Then, A, B and C together will empty this tank.

Now, work done by A, B and C together

5. A tank is filled in 10 hrs 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? (SSC Grad 2000)

(a) 10 hrs

(b) 40 hrs

(c) 70 hrs

(d) 80 hrs

Explanation:

Let pipe A alone fill the tank in x hrs.

Then, pipe B will fill it in

Pipe C will fill it in

x=70hrs

6. Pipe A can fill a tank in 2hrs, pipe B in 4 hrs and pipe C in 6 hrs. If all the pipes are open, in how many hours the tank will fill?

(a)

(b)

(c) 20 hrs

(d) 3 hrs

Explanation:

Part filled by A in 1 hr

Part filled by B in 1 hr

Part filled by C in 1 hr

Part filled by A+B+C in 1 hr

All the pipes together will fill the tank in  hours .

7. A cistern has 3 pipes A, B and C The pipes A and B can fill it in 5 hr and 6 hr respectively and C can empty it in 3 hr. If the pipes are opened in order at 3 pm, 4 pm and 5 pm respectively at what time the tank be filled?

(a) 6 am

(b) 5 am

(c) 4 am

(d) 7 am

Explanation:

By 5 pm, the water filled by 2 pipes = 2 hr work done by pipe + 1 hr work done by pipe B

After 5 pm all the three pipes are working and the work done by all the 3 pipes 1 hr

After 5pm only of the tank is to be filled time taken in filling

13 hr after 5 pm = 6 am

8. Three pipes A, B and C can fill a tank in 12 hrs. After working at it together for 4 hrs, C is closed and A and B can fill the remaining part in 14 hrs. The number of hours taken by C alone to fill the tank is:

(a) 10 hrs

(b) 12 hrs

(c) 14 hrs

(d) 28 hrs

Explanation:

Part filled in 4 hrs

Remaining part

(A+B)’s 14 hrs work

(A+B)’s 1 hrs work

C’s 1hrs work= (A+B+C)’s 1 hrs work-(A+B)’s 1 hrs work

C alone can fill the tank in 28 hrs.

9. A tank is filled in 2hrs by three pipes A, B and(c) The pipe C is three times 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) 10 hrs

(b) 12 hrs

(c) 18 hrs

(d) 80 hrs

Explanation:

Let pipe A alone fill the tank in x hrs.

Then, pipe B will fill it in

Pipe C will fill it in

x=18hrs.

10. Two pipes A and B can fill a cistern in 24min and 30min respectively, but a third pipe C can empty the full tank in 12 min. A and B are kept open for 10 min in the beginning and then C is also opened. In what time is the cistern emptied?

(a) 2 hrs

(b)

(c)

(d) 20 hrs