Pipes and Cisterns - Aptitude Questions and Answers Part 2

6. There are two inlets and one outlet to a tank. Inlet A and B take 1.5 hours and 2 hours respectively to fill the tank. While outlet C can empty the entire tank in 30 minutes. The gardener decides to open Inlet A at 8 am when he arrives on duty and Inlet B one hour later. Outlet C is opened at 10 am. What will be the time by his watch when the tank will be entirely empty again?

a. 1.25 pm
b. 12 pm
c. 12.12 pm
d. 12.28 pm

Answer: c. 12.12 pm

Explanation:

Let the tank get empty in T hours counting from 8 am.

A is on for T hours and work done by A = Work in 1 hour x T hours =T=2T
1.53
Similarly, B starts at 9 am i.e. it's on for (T-1) hours & work done is =T-1
2
Similarly, C starts at 10 am i.e. for (T-2) hours & work done is =T-2=2(T-2)
1/2
Initially tank is empty and after T hours too, it is empty. So, total work done is 0.
∴2T+T-1- 2(T - 2) = 0
32
∴ T =21hours = 4.2 hours = 4 hours 12 minutes
5
This time is needed for tank to get empty.
Exact time will be 4 hours 12 min from 8 am = 12.12 pm


7. Pipes A and B can fill a tank together in 6 hours. When Pipe C is also open, the tank can be filled in 5 hours by 3 pipes together. Pipe A's efficiency is double of Pipe B. How long will Pipe B and C take to fill the tank entirely?

a. 9.75 hours
b. 10. 90 hours
c. 11.25 hours
d. 12.90 hours

Answer: c. 11.25 hours

Explanation:

Let Pipe A, B and C fill the tank individually in A, B and C hours respectively.

Tank filled by Pipe A, B and C together in 1 hour =1=1+1+1
5ABC
Tank filled by Pipe A and B together in 1 hour =1=1+1
6AB
Tank filled by C in 1 hour =1- (1+1) =1-1=1
6AB6530
But A is twice as fast as B. Hence to do same work, time taken by A is half the time taken by B.
∴ A = ½B
∴1+1=1
½BB6
∴1=1hours
B18
Tank filled by B and C in one hour =1+1=1+1=8
BC183090
∴ Tank can be filled in90= 11.25 hours
8


8. Tap A and B can fill a cistern together in 2.4 hours. The water from Tap A flows at the rate of 100 litre per hour to fill the cistern while Tap B has the capacity to fill the entire cistern in just 4 hours. Find how much water can the cistern hold?

a. 500 litres
b. 600 litres
c. 1000 litres
d. 1200 litres

Answer: b. 600 litres

Explanation:

Let Tap A fill the cistern completely in A hours.

So in 1 hour it fills1amount of the cistern
A
Also in 1 hour Tap B fills1amount of the cistern
4
Together they fill the cistern in 2.4 hours
So, in 1 hour together they'll fill1amount of the cistern
2.4
Also in 1 hour cistern filled by both is given by1+1=1
A42.4
∴1=1-1=1
A2.446
∴ Pipe A can fill 1/6th tank in 1 hour
∴ Pipe a fills the tank completely in 6 hours.
It has a rate of 100 litre water per hour,
So, in 6 hours it gives out 6 x 100 = 600 litres
In 6 hours cistern is full, so capacity = 600 litres


9. A tank has 2 inlets and 1 outlet. The inlets P and Q can fill the tank in 15 hrs and 10 hours respectively. The outlet R take 30 hours to empty the tank. The gardener's son opens all the three pipes by mistake. The gardener realizes this after 2 hours and closes the outlet R so that the tank can be filled. Due to this mistake of his son, how much extra time will be required to fill the tank?

a. 18 minutes
b. 24 minutes
c. 1 hour 20 minutes
d. 2 hours 15 minutes

Answer: b. 24 minutes

Explanation:

In 1 hour, tank filled by Pipe P =1
15
In 1 hour, tank filled by Pipe Q =1
10
In 1 hour, tank emptied by Pipe R =1
30
Normally if Pipe R is closed, then
In one hour tank filled  =1+1=5
151030
So entire tank gets filled in30= 6 hours
5
When Pipe P, Q & R is open, in 1 hour tank filled  =1+1-1=4
15103030
In 2 hours, 2 x4=8amount of tank is filled
3030
Remaining tank = 1 -8=22
3030
This is filled by Pipe P and Q only
In 1 hour,5amount of tank is filled
30
In ? hours,22amount of tank is filled
30
∴ ? hours =22/30=22= 4.4 hours
5/305
So total time taken = 2hours + 4.4 hours = 6.4 hours
Extra time taken = 6.4 - 6.0 = 0.4 hours = 24 minutes


10. Three pipes A, B and C when opened simultaneously can fill a tank in 6 hours. C is closed after 2 hours while A and B fill the remaining tank in 7 hours. How long will C take to fill the tank alone?

a. 10 hours
b. 12 hours
c. 13 hours
d. 14 hours

Answer: d. 14

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