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Question 5.

The rate of water flow through three pipes A, B and C are in the ratio 4: 9: 36. An empty tank can be filled up completely by pipe A in 15 hours. If all the three pipes are used simultaneously to fill up this empty tank, the time, in minutes, required to fill up the entire tank completely is nearest to

A
B
C
D
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Text Explanation
Let the rate of flow of water from pipe A be $4x$ units per hour. From the ratio of the rates of flow of water (4:9:36), we have that the rate of flow of water from pipe B should be $9x$ units per hour, and from pipe C should be $36x$ units per hour.
Since pipe A fills the empty tank in 15 hours, the capacity of the tank must be $15\times 4x = 60x$ units.
When all three pipes work together, their combined capacity would be $4x+9x+36x = 49x$ units per hour.
Therefore, the time it would take for the three pipes to fill the empty tank working together is:  $\dfrac{60x}{49x}$ hours
In minutes, this time is equivalent to $\dfrac{60x}{49x}\times 60 \approx 73.47$ minutes.
Option A is the closest, and is the correct answer.
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