Two pipes A and B can fill a tank in 40 min and 60 min respectively. Find the time taken by the pipes A, B and C to fill the tank, if tank C is emptying pipe whose efficiency is 25% more than that of pipe B.

Correct Answer: 48 min

Step-by-Step Explanation:

Step 1: Determine the total capacity of the tank.
Let us assume the total capacity of the tank to be the Least Common Multiple (LCM) of the time taken by pipes A and B.
LCM of 40 minutes and 60 minutes = 120 units.

Step 2: Calculate the efficiency (work done per minute) of each pipe.
Efficiency of Pipe A = Total Capacity / Time taken by A
$\text{Efficiency of A}=\frac{120}{40}=3\text{ units/min}$

Efficiency of Pipe B = Total Capacity / Time taken by B
$\text{Efficiency of B}=\frac{120}{60}=2\text{ units/min}$

Step 3: Calculate the efficiency of Pipe C.
Pipe C is an emptying pipe whose efficiency is 25% more than that of Pipe B.
$\text{Efficiency of C}=2+\left(25\text{\% of}2\right)$
$\text{Efficiency of C}=2+(0.25\times 2)=2+0.5=2.5\text{ units/min}$
Since Pipe C is an emptying pipe, its net work contribution is negative: -2.5 units/min.

Step 4: Calculate the combined efficiency of Pipes A, B, and C working together.
$\text{Net Efficiency}=\text{Efficiency of A}+\text{Efficiency of B}-\text{Efficiency of C}$
$\text{Net Efficiency}=3+2-2.5=2.5\text{ units/min}$

Step 5: Find the total time taken to fill the tank.
$\text{Time taken}=\frac{\text{Total Capacity}}{\text{Net Efficiency}}$
$\text{Time taken}=\frac{120}{2.5}=48\text{ minutes}$

Thus, the time taken by pipes A, B, and C together to fill the tank is 48 min.