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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.

Correct Answer: 32 min

Explanation:

Given that the diameters of the three pipes are 2 cm, 3 cm and 4 cm


From the given data,


Amount of water from three pipes is 4 units, 9 units and 16 units.


Let the capacity of cistern be 'p' units.


∴ p/58 = 16


⇒ p = 928 units.


 


In 1 minute, quantity to be filled by 3 pipes = 29 units


∴ Total time required = 928/29 = 32 minutes.


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