Explanation:
To find the reduced price per kilogram of the article, follow these steps:

1. Determine the original price per kilogram:

Let \( P \) be the original price per kilogram in Naira.

The reduction of 25% means the new price is 75% of the original price. So, the reduced price per kilogram is:
\[
0.75P
\]

2. Calculate how much more of the article can be bought with the reduced price:

With the original price, the amount of article that can be bought for N500 is:
\[
\frac{500}{P} \text{ kilograms}
\]

With the reduced price, the amount of article that can be bought for N500 is:
\[
\frac{500}{0.75P} \text{ kilograms}
\]

3. Find the difference in the amount of article bought:

The difference in the amount of article that can be bought is:
\[
\frac{500}{0.75P} - \frac{500}{P}
\]

Simplify this expression:
\[
\frac{500}{0.75P} = \frac{500 \times 4}{3P} = \frac{2000}{3P}
\]
\[
\frac{500}{P} = \frac{500}{P}
\]
\[
\frac{2000}{3P} - \frac{500}{P} = \frac{2000 - 1500}{3P} = \frac{500}{3P}
\]

This difference is given as 50 kilograms:
\[
\frac{500}{3P} = 50
\]

4. Solve for \( P \):

Rearranging the equation to find \( P \):
\[
500 = 150P
\]
\[
P = \frac{500}{150} = \frac{10}{3} \approx 3.33
\]

So, the reduced price per kilogram, which is 75% of the original price, is:
\[
0.75 \times \frac{10}{3} = \frac{7.5}{3} = 2.50
\]


The reduced price per kilogram is N2.50.

The correct answer is C. N2.50.