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

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.