Question: 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?

7:20 am

6:00 am

6:40 am

5:00 am

Answer:

6:40 am

Solution:

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

Question: 12 -

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?

2 hrs 55 min

4 hrs 48 min

3 hrs 40 min

5 hrs 53 min

Answer:

5 hrs 53 min

Solution:

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.

Question: 13 -

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?

1:35 pm

2:40 pm

1:00 pm

12:00 pm

Answer:

2:40 pm

Solution:

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
Here, -ve sign indicates C empty the tank.
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

Question: 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

112/5

12

14

21/2

Answer:

112/5

Solution:

Volume of cylinder = π r² h

π r² h = 11 litres = 11000 cm³

Or  = 11000 cm³

h = 

h =  = 22cm