Question

How many minutes can a cistern be filled by 3 pipes, whose diameters are 20 cm, 30 cm and 60 cm working together, if the largest alone can fill it in 49 minutes?

Answer 1

In one minute the pipe of 2cm diameter fills 1/61  of the cistern.
In one minute the pipe of 1cm diameter fills 1/61* 1/4   of the cistern
In one minute the pipe of 11/3 cm diameter fills 1/61* 4/9   of the cistern
In one minute (1/61+1/(61*4)+4/(61*9))=1/36   of the cistern is filled.
The whole cistern is filled in 36 minutes.

Answer 2

Answer:

19.168 minutes.

Step-by-step explanation:

The largest alone will fill in 49 min

The amount of water flowing in by each pipe being proportional to the square of its diameter

So, In one minute the pipe of 60 cm diameter fills 1/60  of the cistern.

Given that the diameters of the three pipes are 20 cm, 30 cm and 60 cm

From the given data,

Amount of water from three pipes is 400 units, 900 units and 3600 units.

Let the capacity of cistern be 'p' units.  

$\frac{p}{49}=1600$

$p=78400$

p = 78400

In 1 minute, quantity to be filled by 3 pipes = 4090 units

∴ Total time required = $\frac{78400}{4090}$= 19.168 minutes.