# Aptitude Pipes and Cisterns Test Paper 3

11) A can fill a tank in 8 hours, B can fill the same in 12 hours, and C can fill the tank in 24 hours. If they are open at 2 am, 3 am, and 4am respectively, then at what time the tank will be completely fill?

1. 5:00 am
2. 6:00 am
3. 6:40 am
4. 7:20 am

ATQ,

At 2am: A starts and fill the tank in 8 hours.
At 3am: B starts and fill the tank in 12 hours.
At 4am: C starts and fill the tank in 24 hours.

Let the capacity of the tank = LCM of (A's, B's, and C's time)
Now, LCM of 8, 12, and 24 is 24.
i.e., the capacity of the tank = 24 litre

Now, A's one hour work = capacity of the tank/ time taken by A.
A's one hour work = 24/ 8 = 3litre/hour.
B's one hour work = 24/12 = 2litre/hour.
C's one hour work = 24/24 = 1litre/hour.

ATQ, between 2am to 3am, only A works = 3 unit
Between 3am to 4am, A and B works = 3+2 = 5 unit
Total work done till 4 am is 5+3 = 8 unit
Then the remaining work after 4am = 24-8 = 16unit
Now,
Between 4am to 5am, A, B, and C works = 3+2+1 = 6unit/hr

To complete the 16 unit work it requires 16/6 = 2[2/3], or 2:40min
That means the total work will complete at 4am+2hr+40min= 6:40 am

12) Two pipes A and B individually can fill a tank in 15 hours, and 12 hours respectively, and C can empty the full tank in 4 hour. If all three pipes are open at 8, 9, and 11 am respectively. At what time tank will be completely empty?

1. 2:40 pm
2. 1:00 pm
3. 12:00 pm
4. 1:35 pm

ATQ,

At 8am: A starts and fill the tank in 15 hours.
At 9am: B starts and fill the tank in 12 hours.
At 11am: C starts and empty the tank in 4 hours.

Let the capacity of the tank = LCM of (A's, B's, and C's time) Now, LCM of 15, 12, and 4 is 60.
i.e., the capacity of the tank = 60 litre

Now, A's one hour work = capacity of the tank/ time taken by A.
A's one hour work = 60/ 15 = 4litre/hour.
B's one hour work = 60/12 = 5litre/hour.
C's one hour work = 60/4 = 15litre/hour.

ATQ, between 8am to 9am, only A works = 4 units
Between 9am to 10am, A and B works = 4+5 = 9 units
Between 10am to 11am, A and B works = 4+5 = 9 units
Total work done till 11 am is 4+9+9 = 22 units
Now,
Between 11am to 12am, A, B, and C works = 4+5-15 = -6unit/hr
That means after 11 am, every hour the tank will be empty by 6 units.

Now, we have to empty the 22 unit water that is stored till 11 am
So, the tank can be empty in 1 hour = 6 unit
Or, to empty 1unit water it requires 1/6 hour.
Or, 22 unit = (1/6) * 22 = 11/3
Or, 22 unit water can be empty in 3[2/3], or 3 hour + (2/3)*60 hour
Or, 3hour: 40min

That means the water that is stored till 11 am will be empty in 3hour: 40min

So, the time which requires to empty the tank is 11 hour+3 hour+40min = 2:40pm

8) A tank has two pipes. The first pipe can fill it in 45 minutes and the second can empty it in 1 hour. In what time will the empty tank be filled if the pipes be opened one at a time in alternate minutes?

1. 2 hrs 55 min
2. 3 hrs 40 min
3. 4 hrs 48 min
4. 5 hrs 53 min

Let pipe A can fill a tank in 45 minutes
Pipe B can empty in 1 hour = 60 minutes.

Now, take LCM of A and B to find the capacity of the tank

LCM of A (45) and B (60) = 180
That means assume the capacity of tank is 180 litres

Now, 1 minute work of A = 180/45 = 4 units
Now, 1 minute work of B = 180/60 = - 3 units

Here ?ve indicates empty tank per minute
But ATQ, the pipes are open alternatively, that means the net filling of tank in 2 minutes = 4-3 = 1 unit

Now, 176 units will be filled in 176*2 = 352 minutes.

Now, the remaining 4 litres will be filled in next 1 minute
i.e., 352 + 1 = 353 min = 60*5 = 300 + 53

Therefore, the time taken to fill the tank = 5 hrs + 53 min.

14) A cylindrical tank of diameter 25 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop by (use π =22/7).

1. 10 cm
2. 12cm
3. 14 cm
4. 22 cm

Volume of cylinder = π r2 h

π r2 h = 11 litres = 11000 cm3

Or = 11000 cm3

h =

h = = 22cm

Therefore, the water level in the will be drop by 222/5 cm

15) Two pipes can separately fill a tank in 20 hrs and 30 hrs respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which of the water supplied by both the pipes per hour leak out. What is the total time to fill the tank?

1. 12 hrs.
2. 14 hrs.
3. 18 hrs.
4. 16 hrs.

Let pipe A can fill a tank in 20 hours
Pipe B can empty in 1 hour = 30 hours

Now, take LCM of A and B to find the capacity of the tank

LCM of A (20) and B (30) = 60 litres
That means assume the capacity of tank is 60 litres

Now, A can fill the tank in one hour = 60/20 = 3 litres/hr.
B can fill the tank in one hour = 60/30 = 2 litres/hr

If (A+B) both open together then the tank will be filled in 60/ (2+3) = 12 hours.

If both pipes open together then to fill 1/3 part of the tank they requires 12/3 = 4 hours

Or, in the 4 hours, A+B together will fill 4* 5 = 20 litres.
Now the remaining = 60-20 litres

ATQ, (A+B) can fill the tank per hour = 5 litres, but (1/3) of 5 flows out by leakThat means 5/3 litres flow out per hour.

Now, total inlet per hour = 5-= 10/3 litres
Therefore, to fill the remaining 40 litres, both pipes take = 12 hours
Hence, total time to fill the tank = 12+4 = 16 hours

Aptitude Pipes and Cisterns Test Paper 1
Aptitude Pipes and Cisterns Test Paper 2
Pipes and Cisterns Concepts