Question

Three taps  p,q and r can fill a tank in 10,20 and 30 hours respectively. If a is open all the time and q and r are open for one hour each alternatively ,the tank will be fill in

Answer 1

Answer:

7 hours

Step-by-step explanation:

Let volume of drum is V

If

P fill drum in 10 hours then

In 1 hour p fill the drum = (1 / 10) of V = V / 10

Similarly

If

Q fill drum in 20 hours then

In 1 hour Q fill the drum = (1 / 20) of V = V / 20

And

R fill drum in 30 hours then

In 1 hour R fill the drum = (1 / 30) of V = V / 30

Now

If both P and Q are opens for One hour then

Drum fill by both P and Q in 1 hour =  V / 10 +  V / 20 = 3V / 20

And

If both P and R are open for One hour then

Drum fill by both P and R in 1 hour =   V / 10 +   V / 30 = 4V / 30

Thus

In first hour when P and Q are both open

Drum fill in first hour = 3V / 20

In second hour both P and R open so

Drum fill individual in second hour = 4V / 30

And

Drum fill in both First and Second hour = 3V / 20 + 4V / 30 = 17V / 60

In 3rd hour again both P and Q are open

So

Drum fill in individual in 3rd hour = 3V / 20

And

Drum filled in first 3 hours = drum filled in 2 hours + drum fill in 3rd hour

                                           =  17V / 60 + 3V / 20 = 26V / 60

In forth hour again both P and R are open

So

Drum filled in forth hour individually = 4V / 30

And

Drum filled in first 4 hours = drum filled in 3 hours + drum filled in forth hour

                                            = 26V / 60 + 4V / 30 = 34V / 60

In fifth hour again both P and Q are open

So

Drum filled in fifth hour individually = 3V / 20

And

Drum filled in first 5 hours = drum filled in 4 hours + drum filled in fifth hour

                                            =  34V / 60 + 3V / 20 = 43V / 60

In 6th hour again P and R are open

So

Drum filled in sixth hour individually = 4V / 30

And

Drum filled in first 6 hours = drum filled in 5 hours + drum filled in sixth hour

                                            =  43V / 60 + 4V / 30 = 51V / 60

In fifth hour again both P and Q are open

So

Drum filled in seventh hour individually = 3V / 20

And

Drum filled in first 7hours=drum filled in 6 hours+drum filled in seventh hour

                                          = 51V / 60 + 3V / 20 = 60V / 60 = 1V = V

So

After 7 hours the drum completely filled.