Question

A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled ? (1) 121 minutes (2) 110 minutes (3) 115 minutes (4) 120 minutes​

Answer 1

Answer:

(3) 115 minutes

Step-by-step explanation:

Given,

A cistern is provided with two pipes A and B

A can fill the tank in 20min

B can empty the tank in 30min

The part of tank filled by pipe A in 1 min = $\frac{1}{20}$

The part of tank filled by pipe B in 1 min = $\frac{1}{30}$

The part of tank filled by two pipes alternatively in 2 mins

= $\frac{1}{20}$- $\frac{1}{30}$

= $\frac{3-2}{60}$

= $\frac{1}{60}$

Therefore,

It takes 2 min to fill 1 litre

If both pipes works continuosly..Then,

The the time taken to fill 57 litres is

= 57×2

= 114 mins

Next, at the 115th minute, remaining three litres are filled by the pipe A

So, it takes 115 mins to fill the tank!

Answer 2

Answer: 115 Minutes

Step-by-step explanation:

Let us suppose that capacity of tank is 60 ltr. (LCM of 20 and 30)

Now,

A can fill the tank  in 20 minutes,

It means rate of A  = 60/20 = 3 ltr./minutes.

B can empty the tank in 30 minutes,

It means working rate of B = 60/30 = 2 ltr./Minutes

Here given that, both pipes be kept open alternately  for one minute each.

It means that,

First we open A for 1  minute and close.

Then, open B for 1 minute and close

Again open A  for 1 minute and close,

open B  for 1 ...

And so on

A - B + A - B  + A - B ......................

Let us Discuss first two minutes:-

Open A  for 1 minutes;- Tank filled 3 ltrs.

Open B for next 1 minutes:- Tank got empty = 2 ltrs.

Total water in 2 minutes = 3(Filled) - 2(Got empty)

                                        = 1 ltr.

Here we can conclude that, We are filling 1 ltr. of tank in 2  minutes.

So, 57 ltr. of tank can be fillted 57 × 2 = 114.

Just after this 144 minutes,  A will be opened and it will fill the tank with 3ltrs. in next one minutes. So after 57 ltrs. tank will be filled upto 57+3=60

ltrs.

So total time taken = 114 + 1

                                = 115 Minutes.