Wipro Pipes & Cisterns Quiz-1

ANSWER: 22.27 minutes

Explanation:

In 1 min cistern filled by tap A: 35 mins

In 1 min cistern emptied by tap B: 55 mins

In 1 min cistern filled by tap A and B : (1/35) - (1/55) = 4/385

In 35 mins, 35 x (4/385) = 4/11 amount of Cistern is filled

Remaining Cistern: 1 - (4/11) = 7/11

This is filled by tap A only

In 1 min, 1/35 amount of cistern is filled = In ? min, 7/11 amount of cistern is filled

? min = (7/11)/(1/35) = 22.27 mins = Time to fill after tap B is closed

 

ANSWER: 16 minutes

Explanation: 


In 1 hr, tank filled by Pipe A = 1/25 hrs

In 1 hr, tank filled by Pipe B = 1/5 hrs

In 1 hrs tank emptied by Pipe C = 1/50 hrs

Now if Pipe C is closed then

In 1 hr tank filled: (1/25) + (1/5) = (6/25)

So entire Pipe gets filled in: 25/6 = 4.33 hrs

Now is Pipe A, B and C are open tank will be filled in: (1/25) + (1/5) - (1/50) = (11/50)

In 2 hrs, 2x(11/50) = (11/25) amount of tank is filled

Remaining tank: 1 - (11/25) = 14/25

This is the pipe filled by A sn B only

In 1 hr 6/25 amount of tank is filled

In ? hr 14/25 mount of tank is filled

? hr = (14/25)/(6/25) = 14/6 = 2.33 hrs

Total time taken = 2 hr + 2.33 hrs = 4.33

Extra time taken = 4.33 hrs - 4.17 hrs

= 16 mins

ANSWER: 3750 litres

Explanation: 
Let pipe P fill the tank in P hrs

So in 1 hr 1/P amount of tank is filled

So in 1 hr Pipe Q fille 1/12 amount of tank

Together they can the tank in 8.4 hrs

So in 1 hr together they can fill the 1/8.4 amount of tank

So in 1 hr tank is filled by both in 1/A + 1/12 = 1/8.4

1/A = (1/8.4) - (1/12) =1/28

Pipe P can fill 1/28 tank in 1 hr

Pipe P fills the tank completely in 28 hrs

It has a rate of 150 litters per hr

So in 28 hrs, it gives out 28x150 = 3750 liters

In 6 hrs tank is filled so capacity is 3750 liters

Explanation:
Tank filled or work done by P in 1 hour = 1/22
Tank filled or work done by Q in 1 hour (Q takes 11 hrs more than P) = 1/33
Tank filled or work done by both pipes in 1 hour = (1/22) + (1/33) = (5/66)
So the entire tank is full in 66/5 = 13 (1/5) hours

Explanation:
Tank filled by A in 1 hour = 1/38
Tank filled by B in 1 hour (A takes 38 hrs, so B would take 19 hrs) = 1/19
Tank emptied by leakage C in 1 hour = 1/133
Tank filled by all 3 openings together in 1 hour = (1/38) + (1/19) - (1/133)

Making denominators common,
Tank filled by all 3 pipes together in 1 hour = (3.5/133) + (7/133) - (1/133) = (9.5/133) = 1/14
So the entire tank is full in 14/1 = 14 hours -------------> Inverse or reciprocal of 1/14

Explanation:
Normally, Pipe P can fill the cement tank in 24 hours. So in 1 hour, it fills = 1/24 part of tank
Due to leak, Pipe P can fill the tank in 36 hours. So in 1 hour it actually fills = 1/36 part of tub
∴ Water removed by the leak in 1 hour = (1/24) - (1/36) = (1/72)
∴ Leak empties the tank in 72 hours.

Explanation:

Let Tap A take T minutes to fill the tank alone.
Since Tap A is 5 times faster than Tap B, Tap B takes 5 times more time.
So time taken by Tap B = 5 T minutes
Also, 5T-T = 32 ------------------- Given
∴ T = 8 minutes = Time taken by A
Time taken by B = 5 x 8 = 40 minutes.
In 1 min, A + B fills = (1/8) + (1/40) = (3/20) part of tank
So entire tank is filled in 20/3 minutes -------------> Inverse or reciprocal of 3/20

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/1.5 = 2T/3
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)/(1/2) = 2(T-2)
Initially tank is empty and after T hours too, it is empty. So, total work done is 0.
∴ (2T/3) + (T-1)/2 - 2(T - 2) = 0
∴ T = 21/5 hours = 4.2 hours = 4 hours 12 minutes
This time is needed for tank to get empty.
Exact time will be 4 hours 12 min from 8 am = 12.12 pm

ANSWER: 8/116.25 part

Explanation:

Tank filled by pipe P is: 1/7.5 hrs

Tank emptied by pipe Q is: 1/15.5 hrs

Tank filled in 1 hrs = (1/7.5) - (1/15.5) = 8/116.25

ANSWER: 21 minutes

Explanation:

Area = work done

Area = πr²

Since it is square of radius when radius or diameter doubles its area becomes 4 times

When area becomes 4 times work done also becomes 4 times

So time taken by tap with diameter 2d to empty the tank = 84/4 =21 mins