Question

$\large\red{\sf{Question}}$
A cistern has two inlets A and B which can fill it in 12 minutes and 15 minutes respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes are opened together in the empty cistern, then the time taken to fill the cistern completely is
A-20 minutes
B-10 minutes
C-15 minutes
D-5 minutes​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• A cistern has two inlets A and B and one outlet C.

• A can fill it in 12 minutes

• B can fill in 15 minutes.

• An outlet C can empty the full cistern in 10 minutes.

Let assume that

• Volume of cistern be V units.

Since, it is given that inlet A fill the cistern in 12 minutes.

So,

$\rm \: Part \: of \: cistern \: filled \: in \: 1 \: minute = \dfrac{V}{12}$

Now, further given that inlet B fill the cistern in 15 minutes.

So,

$\rm \: Part \: of \: cistern \: filled \: in \: 1 \: minute = \dfrac{V}{15}$

Now, outlet C empty the cistern in 10 minutes.

So,

$\rm \: Part \: of \: cistern \: empty \: in \: 1 \: minute = \dfrac{V}{10}$

So, if three pipes are opened together, then

$\rm \: Part \: of \: cistern \: filled \: in \: 1 \: minute$

$\rm \: = \: \dfrac{V}{12} + \dfrac{V}{15} - \dfrac{V}{10}$

$\rm \: = \: \dfrac{5V + 4V - 6V}{60}$

$\rm \: = \: \dfrac{9V - 6V}{60}$

$\rm \: = \: \dfrac{3V}{60}$

$\rm \: = \: \dfrac{V}{20}$

So, Time taken to fill the cistern = 20 minutes.

So, option A is correct.

Answer 2

UNDERSTANDING CONCEPT :-

• The individual time needed for each pipe for filling or emptying the cistern is given. So we can calculate the part of the cistern filled in one hour for both inlet pipes, add them and subtract the part emptied by outlet pipe in one hour. Now we found part of the cistern filled by all three pipes in one hour.Using this we found the time required to fill the whole cistern.

QUESTION :-

• A cistern has two inlets A and B which can fill it in 12 minutes and 15 minutes respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes are opened together in the empty cistern, then the time taken to fill the cistern completely

TO FIND :-

the time taken to fill the cistern completely = ?

SOLUTION :-

Calculate the amount of cistern inlet B will fill

in 1 minute using formula 1

Since inlet B can fill a cistern in 15 minutes,

inlet B will fill 1/15 of the cistern

in 1 minute

Calculate the amount of cistern inlet C will empty in 1 minute using formula 1

Since inlet C can empty a cistern in 10 minutes, inlet C will empty 1/10 of the cistern in one minute

Calculate the amount of tank filled in 1 minute while keeping all the three taps open simultaneously using

formula 1 and equation 1, 2,3

Since inlet A can fill a cistern in

12 minutes, inlet B can fill a cistern in 15 minutes and inlet C an empty a cistern in 10 minutes, the amount of tank pipe that will be filled while keeping all the three tap open simultaneously in 1 minute = 1/12 + 1/15 - 1/10

= 1/12 + 1/15 - 1/10

= 5/60 + 4/60 - 6/60

= 9 - 6 /60

= 3/60

= 1/20

Therefore, total amount of time all the taps will take to fill the tank completely if all of them are opened together = 1/20

= 1 × 20/1

= 20

Thus, all the three taps will take

20 minutes to fill the tank completely if all of them are opened together.