Two pumps, X and Y, can independently fill a water reservoir in 40 minutes and 60 minutes, respectively. A drainage outlet, Z, evacuates water at a rate that is 25% more efficient than pump Y's filling rate. How long will it take to fill the reservoir if pumps X and Y and drainage outlet Z are all opened simultaneously?

The correct option is 48 min.

Step 1: Calculate the filling rates of pumps X and Y.

Let the total capacity of the reservoir be 1 unit.

Pump X fills the reservoir in 40 minutes. Therefore, pump X's work rate per minute is:

$\text{Rate of X}=\frac{1}{40}$

Pump Y fills the reservoir in 60 minutes. Therefore, pump Y's work rate per minute is:

$\text{Rate of Y}=\frac{1}{60}$

Step 2: Determine the drainage rate of outlet Z.

Drainage outlet Z evacuates water at a rate that is 25% more efficient than pump Y's filling rate. This means Z's drainage rate is 125% (or 1.25 times) pump Y's rate:

$\text{Rate of Z}=1.25\times \text{Rate of Y}$

Expressing 1.25 as a fraction $\frac{5}{4}$:

$\text{Rate of Z}=\frac{5}{4}\times \frac{1}{60}=\frac{5}{240}=\frac{1}{48}$

Step 3: Calculate the combined net filling rate.

When pumps X and Y are filling while outlet Z is draining simultaneously, the net rate of change in water level per minute is:

$\text{Net Rate}=\text{Rate of X}+\text{Rate of Y}-\text{Rate of Z}$

Substituting the respective rates into the equation:

$\text{Net Rate}=\frac{1}{40}+\frac{1}{60}-\frac{1}{48}$

To combine these fractions, find the Least Common Multiple (LCM) of the denominators 40, 60, and 48, which is 240:

$\text{Net Rate}=\frac{6+4-5}{240}=\frac{5}{240}=\frac{1}{48}$

Step 4: Calculate total time to fill the reservoir.

The total time required to completely fill the reservoir (1 unit) at the net rate of $\frac{1}{48}$ per minute is given by:

$\text{Total Time}=\frac{1}{\text{Net Rate}}=\frac{1}{1/48}=48\text{minutes}$

Therefore, it will take 48 minutes to fill the reservoir completely.