The rectangular piece of iron sheet is rolled into a cylinder, which means the length of the rectangle becomes the circumference of the cylinder. The given length of the rectangle is 100 cm, which becomes the circumference of the cylinder.

Circumference of the cylinder = 100 cm

To find the radius of the cylinder, we can use the formula for the circumference of a circle:

Circumference = 2?r

100 = 2?r

r = 50 / ? cm

Now, let`s calculate the area of the outer surface of the cylinder:

Outer surface area = 2?rh

Since the height of the cylinder is also given as 50 cm, we can substitute the values:

Outer surface area = 2? * (50 / ?) * 50 = 5000 cm²

To convert the area to square meters, we divide by 10000:

Outer surface area = 5000 cm² / 10000 = 0.5 m²

Finally, we multiply the area by the cost per square meter:

Cost of painting the outer surface = 0.5 m² * Rs. 50/m² = Rs. 25.00

Therefore, the correct answer is Rs. 25.00, which aligns with option (a).