Question

In what time would a cistern be filled by three pipes which diameters are 2 cm, 3 cm and 4 cm running together, when the largest alone can fill it is 58 minutes? The amount of water flowing in each pipe is proportional to the square of its diameter.
A) 26 min
B) 32 min
C) 36 min
D) 42 min

Answer 1

Given: diameters are 2 cm, 3 cm and 4 cm

To find: In what time would a cistern be filled by three pipes?

Solution:

• Now we have given that  the largest alone can fill it is 58 minutes and the diameters are 2 cm, 3 cm and 4 cm running together.

• So now:

• Volume of three pipes working together is equal to the volume of the largest pipe working alone .

• We also know that volume = capacity x time

• Capacity of all three pipe is:

                = 2^2 + (3)^2 + 4^2

                = 4 + 9 + 16

                = 29

• Let the capacity of cistern be 'p' units.

• Then p/58 = 16

                p = 928 units.

• In 1 minute, quantity to be filled by 3 pipes will be 29 units .

• So the Total time required is:

               928/29 = 32 minutes.

Answer:

           In 32 minutes  a cistern would be filled by three pipes.