The volume of a wall whose height is 10 times its width and whose length is 8 times its height is 51.2 m$$^3$$ . What is the cost(in ₹) of painting the wall on one side at the rate of ₹100/ m$$^2$$ ?

Let the width of the wall = b

Height of the wall = 10b

Length of the wall = 8 x Height = 8 x 10b = 80b

Volume of the wall = 51.2 m$$^3$$

length x width x height = 51.2

80b x b x 10b = 51.2

8000b$$^3$$ = 512

b = $$\frac{8}{20}$$

b = $$\frac{2}{5}$$ m

Area of one side of the wall = length x height = 80b x 10b = 800b$$^2$$ = 800 x $$\frac{4}{25}$$ = 128 m$$^2$$

The cost of painting the wall on one side at the rate of ₹100/ m$$^2$$ = 128 x 100 = ₹12800

Hence, the correct answer is Option A