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

The correct option is 73.

To find the time required to fill the tank when all three pipes are used simultaneously, we can break the problem down into simple steps based on the rates of water flow.

Step 1: Understand the flow rates of the pipes
The rates of water flow through the three pipes A, B, and C are given in the ratio 4 : 9 : 36. We can express the individual flow rates in terms of a constant variable, $r$:
Flow rate of pipe A = $4r$
Flow rate of pipe B = $9r$
Flow rate of pipe C = $36r$

Step 2: Determine the total capacity of the tank
An empty tank can be completely filled by pipe A alone in 15 hours. The capacity of the tank can be calculated as the product of the flow rate of pipe A and the time it takes:

$\text{Total Capacity}=\text{Flow rate of A}\times \text{Time taken}$

$\text{Total Capacity}=4r\times 15\text{ hours}=60r$

Step 3: Calculate the combined flow rate
When all three pipes are used simultaneously, their combined flow rate is the sum of their individual flow rates:

$\text{Combined Flow Rate}=4r+9r+36r=49r$

Step 4: Calculate the time taken to fill the tank
The time required to fill the tank completely with all three pipes open is the total capacity divided by the combined flow rate:

$\text{Time (in hours)}=\frac{60r}{49r}=\frac{60}{49}\text{ hours}$

Step 5: Convert the time into minutes and round to the nearest integer
To convert hours to minutes, multiply the fraction by 60:

$\text{Time (in minutes)}=\frac{60}{49}\times 60=\frac{3600}{49}\text{ minutes}$

Performing the division:

$\frac{3600}{49}\approx 73.47\text{ minutes}$

Rounding 73.47 to the nearest integer gives 73 minutes.