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

Correct Answer: Option 1 (73)

Step-by-Step Explanation:

1. Understand the given data:
We are given that the rate of water flow (efficiency) through three pipes A, B, and C are in the ratio 4 : 9 : 36.
Let the flow rate of pipe A = 4 units/hour
Let the flow rate of pipe B = 9 units/hour
Let the flow rate of pipe C = 36 units/hour

2. Calculate the total capacity of the tank:
We are given that Pipe A alone can fill the empty tank completely in 15 hours.
Total capacity of the tank = Rate of Pipe A × Time taken by Pipe A

$\text{Capacity}=4\times 15=60\text{units}$

3. Calculate the combined rate of all three pipes:
When pipes A, B, and C are used simultaneously, their combined flow rate is:

$\text{Combined Rate}=4+9+36=49\text{units/hour}$

4. Calculate the time required to fill the tank (in hours):
Time taken to fill the tank = Total Capacity / Combined Rate

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

5. Convert the time from hours to minutes:
Since 1 hour = 60 minutes, we multiply the time in hours by 60:

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

Performing the division:

$\frac{3600}{49}\approx 73.469\text{minutes}$

Rounding off to the nearest integer gives 73 minutes.